Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. October 19, 2004. 15 of Sipser book) Q16. pdf), Text File (. A prunable state in a DFA is some state that is never entered while processing any input string. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. Since EQ DFA is decidable, we assume that is an algorithm M (i. Let Lpal2 be the language wwRvvR:w, v E E' a. (In each transition, we can read the top of both stacks and push something on top of both stacks, if we choose. Proof: A DFA accepts some string iff reaching an accept state from the start state by >traveling along the arrows of the DFA is possible. Show that the collection of decidable languages is closed under union. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Sipser provides an algorithm for ALL NFA that runs in nondeterministic space O(n), so ALL. Let LEN_CFG = { | G Is A CFG, K Elementof Z^noneg, And L(G) Intersection Sigma^k Notequalto (where Sigma Is The Alphabet Of G)}. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and undecidable languages The halting problem. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. 10 Marks (PROBLEM 5. Show that ALL NFA = fhMi: L(M) for the NFA Mwhose input alphabet is gis in PSPACE. Show that ETM, the complement of. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. CSCI 2670 Introduction to Theory of Computing. Consider the following algorithm for deciding whether a given non-empty string s of length n belongs to A∗: For ev-ery possible way of splitting s into non-empty substrings s =. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Let build M0as follows: M0= \On input w: 1. 2) Let INFINITE DFA = { | A is a DFA and L(A) contains an infinite number of strings}. Express this problem as a language and show that it is decidable. Transcription. Let Lpal2 be the language wwRvvR:w, v E E' a. 64 Let N be an NFA with k states that recognizes some language A. Please attach your answer to this in the file Spiral. (Hint: Look at the proof for EDFA to get an idea. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. IScan the input string hG;wi, determining whether the input constitutes a valid CFG. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. Creating DFA to prove closure properties. pdf), Text File (. 3 Let ALLDFA = { | A is a DFA that recognizes (*}. Show that ALLDFA is decidable. If T accepts, “accept”. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. pdf using cvssubmit. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. Keeping your cool. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. Run M1 on w. Then, let M be a DFA that. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. Department of Computer Science COMPSCI 350 Assignment 2 Due: May 15 1. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. Create a DFA B such that L(B) = Σ * 2. 24 on page 88 in the textbook. We show that Sis decidable. (b) Show that L is decidable. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. Showing up. Let A(CFG = { | G is a CFG that generates (}. Q#4 Let LALL ={/M is a TM with i/p ∑ and L(M =∑*} Prove that LALL is not a co Turing recognizable. Say that a variable A in CFL G is usable if it appears in some derivation of some string w G. Give a CFG that (1) Show "all" DFA is decidable. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. Show that ALLDFA is decidable. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. 3) Let a 2-PDA be a pushdown automata with access to 2 stacks. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. Let Lpal2 be the language wwRvvR:w, v E E' a. decidable, a decider for A NTM could be to decide A TM. 3) Consider counting the ordered pairs of integers in the Cartesian plane. Show that ALLDFA is in P. Videos recorded Spring 2014 for CSE355 at Arizona State University. Show that EQ CFG is undecidable. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. Then, let M be a DFA that. Show that ALLDFA is decidable. - 1796261. Submit to the decider for EQ DFA 3. Show that ALL DFA = fhBijBgis DFA and L(B) = gis decidable. pdf - Free download as PDF File (. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. Homework 8Solutions 1. txt) or read online for free. CSCI670CSCI670IntroductiontoTheoryofIntroductiontoTheoryofComputingComputingComputingComputingOctober13005AgendaAgenda•Yesterday-Decidabilityandregularlanguages. Say that a variable A in CFL G is usable if it appears in some derivation of some string w G. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. Let A(CFG = { | G is a CFG that generates (}. Express this problem as a language and show that it is decidable. Gaining skills and applying them well. Give 5 languages that are in the class P. Homework Solution - Set 7 Due: Friday 10/24/08 1. 24 on page 88 in the textbook. , there is a Turing machine M such that M halts and accepts on any input w ∈ A, and M halts and rejects on input input w ∈ A; i. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. Businessman with a ‘golden touch’ who gave the presidential candidate his place in Sin City. P is the class of all languages that are decidable by deterministic multi-tape Turing machines running in polynomial time. (Families Affected by Fetal Alcohol Spectrum Disorder). 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. CS701 mid term paper shared by student. 24 on page 88 in the textbook. Discrete Homework 4 - Travis Montey COT 4210 Homework#4 1 Let ALLDFA = cfw_| A is a DFA and L(A = Show that ALLDFA is decidable a Let T = On input. (Proof idea) IWe construct a Turing machine S to decide the problem. Express this problem as a language and show that it is decidable. A triangle in an undirected graph is a 3-clique. pdf), Text File (. 4 Let AεCFG = { G | G is a CFG that generates ε}. Answer: The universal TM U recognizes A TM, where U is deﬁned as follows: U = "On input hM,wi, where M is a TM and w is a string: 1. (In each transition, we can read the top of both stacks and push something on top of both stacks, if we choose. Show that ALL DFA is decidable. Show that LEN_CFG is decidable. Formulate this problem as a language and show that it is decidable. Prove that ECFG is a decidable language. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. Observe that indeed we cannot copy the proof that EQ DFA is decidable as the the CFL’s are not closed under comple-ment, while the regular languages are. Give a CFG that (1) Show "all" DFA is decidable. Posted by Irfan Khan MSCS on December 18, 2016 at 4:46pm in CS701 - Theory of Computation Mid Term Paper and Final Term Paper; Back to CS701 - Theory of Computation Mid Term Paper and Final Term Paper Discussions. DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. Give a PDA that accepts Lpal2 b. Show that, if A is nonempty, A contains some string of length at most 2k d. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. CSCI 2670 Introduction to Theory of Computing October 19, 2004 Agenda Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. 2 Consider the problem of determining whether a DFA and a regular expression are. Homework 8Solutions. Show that NP is closed under union and concatenation. 4 Let AεCFG = { G | G is a CFG that generates ε}. IScan the input string hG;wi, determining whether the input constitutes a valid CFG. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. Posted by + M. A prunable state in a DFA is some state that is never entered while processing any input string. pdf), Text File (. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. Posted by Irfan Khan MSCS on December 18, 2016 at 4:46pm in CS701 - Theory of Computation Mid Term Paper and Final Term Paper; Back to CS701 - Theory of Computation Mid Term Paper and Final Term Paper Discussions. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Show that ALL DFA is decidable. Step-by-Step Solution: Step 1 of 3. Show that ALLDFA is in P. , looping cannot happen. It will not accept inputs with a 1, but there is no reject state that will cause this DFA to be rejected by the decider. Show that ALLDFA is in P. Express this problem as a language and show that it is decidable. A triangle in an undirected graph is a 3-clique. ) * (3) All the King's Horses, and All the King's Men… Let ALLDFA = { | A is a DFA and L(A) = Σ*} Describe in English what the language ALLDFA consists of. Show that the following language is decidable: SIMPDFA-[A) : A is a DFA with no. Problem 3 (5 Points). Exercise 4. (b) Show that A TM is Turing-recognizable. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. 4 Let AεCFG = { G | G is a CFG that generates ε}. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. 2) Let INFINITE DFA = { | A is a DFA and L(A) contains an infinite number of strings}. Problem 3 (5 points). b Let A be a decidable language and let D be a polytime decider for it. , there is a Turing machine M such that M halts and accepts on any input w ∈ A, and M halts and rejects on input input w ∈ A; i. (b) Show that L is decidable. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. This decider will accept a DFA that does not accept all inputs if, for example, there is no transition for one of the characters in σ. Create a DFA B such that L(B) = Σ * 2. Given a CFG G and a variable A, consider the problem of testing whether A is usable. Show that ALLDFA is in P. Let LEN_CFG = { | G is a CFG, k elementof Z^noneg, and L (G) Intersection sigma^k notequalto (where sigma is the alphabet of G)}. give the pseudocode for function def deciderSUB DFA (G) and discussion of correctness. Show that ALLDFA is in P. By Theorem 4. 15 (a) We want to show that if L 1 and L 2 are decidable, then L 1 [L 2 = L 3 is decidable. We now construct another algorithm M 1 to decide language ALL DFA. DFA with an accepting state in the initial state. A language L belongs to P iff L 2TIME(2n). Show that NP is closed under union and concatenation. Express this problem as a language and show that it is decidable. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. The sea will have its own, its share of tragedies. Able to give care, to show care, to just care. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ. CS701 mid term paper shared by student. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Show that decidable languages are closed under: (a) union (b) concatenation (c) Kleene star (d) complement (e) intersection Answer: For all of these answers, let L, L1 , and L2 be decidable languages, and M , M1 , and M2 be the TM's that decide them. DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ. DFA is decidable. Therefore, A NTM cannot be in PSPACE, so A NTM is not PSPACE-complete. 3) Answer: Consider the following Turing machine M = " on input , where A is a DFA 1. Let build M0as follows: M0= \On input w: 1. Show that T is countable. Show that the set of incompressible strings is un decidable. Thelanguageweareconcernedwithis INFINITEDFA =fhAi: A isaDFAandL(A)isaninﬂnitelanguageg: Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Show that ALL DFA is decidable. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. Step-by-Step Solution: Step 1 of 3. Let build M0as follows: M0= \On input w: 1. Show that ALLDFA is in P. Problem 1 For this problem you may assume the containment diagram in Figure 4. Lecture 32/65: Decidability and Decidable Problems hhp3. Irish: ·sea Proverb: Bainfidh an fharraige a cuid féin amach; beidh a cuid féin ag an bhfarraige. pdf), Text File (. Let A(CFG = { | G is a CFG that generates (}. Prove that ALLDFA is decidable. Turing-recognizable language. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. Solution Outline: (a) Method I: Let D i,i ≥ 1 be the DFA that recognizes the language {1i}. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. Homework Solution - Set 7 Due: Friday 10/24/08 1. Show that ALLDFA is decidable. Hint: First mark each variable that can yield ( by one derivation, then mark those variables that can yield ( by more derivations. P is the class of all languages that are decidable by deterministic single-tape Turing machines running in polynomial time. (In each transition, we can read the top of both stacks and push something on top of both stacks, if we choose. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. Show that the set of incompressible strings is un decidable. Showing up. Since EQ DFAis decidable, there is an algorithm. Able to give care, to show care, to just care. Show that, if A is nonempty, A contains some string of length at most k. A triangle in an undirected graph is a 3-clique. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Construct a PDA P0 such that L(P0) = L(P)\L(M) 3. Show that the SPCP is decidable. 24 on page 88 in the textbook. There is a single "line valid bit" and three bits, B0, B1,. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. Announcements. Give a PDA that accepts Lpal2 b. " Note that U only recognizes A TM and does not decide A TM Because when we run M on w,. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. Full text of "Introduction To Theory Of Computation" See other formats. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Let Cbe the DFA obtained by interchanging accepting and rejecting states of B. FAFASD seeks to spread information, awareness, and hope for families impacted by fetal alcohol spectrum disorder. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Method II: Suppose on the contrary that L is regular. txt) or read online for free. Observe that indeed we cannot copy the proof that EQ DFA is decidable as the the CFL's are not closed under comple-ment, while the regular languages are. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. com - id: 56456d-ZGMxZ. Show that ALLDFA is in P. Note: The next question is a programming question. Since EQ DFAis decidable, there is an algorithm. The Intel 80486 has an on-chip,unified cache. 2) Let INFINITEDFA = { | A is a DFA and L(A) contains an infinite number of strings}. Clearly, hMi2Sif and only if L(M) = L(N). Show that ALLDFA is decidable. Hint: In this case, all the states that are reachable from the start state are final states. 2 Consider the problem of determining whether a DFA and a regular expression are. Give 5 languages that are in the class P. 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. CSCI 2670 Introduction to Theory of Computing. Let SUBSETDFA-A, B L(B)). Show thatALLDFAis decidable. Formulate this problem as a language and show that it is decidable. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. Loading Unsubscribe from hhp3? Show more Show less. October 13, 2005. Step-by-Step Solution: Step 1 of 3. Prove that ALLDFA is decidable. 5 (EQUIVdfa is decidable), the condition L(A)=L(S) is decidable, and so determining if A belongs to ALLdfa is decidable too. CS701 mid term paper shared by student. IScan the input string hG;wi, determining whether the input constitutes a valid CFG. , exhibit a decision procedure for this language): L = {ha,b,ci : a, b and c are regular expressions and a2 ∪b2 = c2. A and B are DFAs and L(A) C Problem 4 (5 points). 17 December cs701 paper CS701 Q#1suppose there is a language L we know that L is Turing. 1 (a) a Yes, because M on input 0100 ends in an accept state. 5 Let ETM = { M | M is a TM and L(M ) = ∅}. What to turn in Save your work in the hw10 folder and turn in the files hw10. Sipser provides an algorithm for ALL NFA that runs in nondeterministic space O(n), so ALL. Run M 1 on w. Let LEN_CFG = { | G Is A CFG, K Elementof Z^noneg, And L(G) Intersection Sigma^k Notequalto (where Sigma Is The Alphabet Of G)}. Yesterday Decidability and regular languages Today Putting things in perspective More on decidability and regular languages Decidability and context free grammars. P is the class of all languages such that if w 2P then there is a deterministic single-tape Turing machine which accepts the string w in polynomial time. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. Let SUBSETDFA-A, B L(B)). import Data. Show that ETM, the complement of. CSCI 2670 Introduction to Theory of Computing. CSCI 2670 Introduction to Theory of Computing October 13, 2005. decidable, a decider for A NTM could be to decide A TM. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. txt) or read online for free. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. CS701 mid term paper shared by student. Show that Th(N,)is decidable. Show that the following language is decidable (ie. Show That SUB_DFA Is Decidable. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. E(dfa) is a decidable language. A triangle in an undirected graph is a 3-clique. Exercise 4. Construct DFA B that recognizes L(A) ii. Show That ALLDFA Is Decidable. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. Since EQ DFAis decidable, there is an algorithm. Therefore, A NTM cannot be in PSPACE, so A NTM is not PSPACE-complete. INTRODUCTION TO THE THEORY OF COMPUTATION. , looping cannot happen. decidable, a decider for A NTM could be to decide A TM. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. Show that ALL NFA = fhMi: L(M) for the NFA Mwhose input alphabet is gis in PSPACE. 2) Let INFINITE DFA = { | A is a DFA and L(A) contains an infinite number of strings}. (b) Show that L is decidable. Else, accept. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. com - id: 56456d-ZGMxZ. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Method II: Suppose on the contrary that L is regular. Using the procedure given in class, convert the regular expression. Use K to check if L(G) is empty. It will not accept inputs with a 1, but there is no reject state that will cause this DFA to be rejected by the decider. CS701 ALL Current Mid Term Papers Fall 2016 And Past Mid Term Papers at One Place from 17 December 2016 to 29 December 2016. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. CSCI 2670 Introduction to Theory of Computing October 13, 2005. Express this problem as a language and show that it is decidable. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Show That The Following. Show that A(CFG is decidable. Prove that ECFG is a decidable language. 2) Let INFINITE DFA = { | A is a DFA and L(A) contains an infinite number of strings}. 5 (EQUIVdfa is decidable), the condition L(A)=L(S) is decidable, and so determining if A belongs to ALLdfa is decidable too. Q#4 Let LALL ={/M is a TM with i/p ∑ and L(M =∑*} Prove that LALL is not a co Turing recognizable. Construct a PDA P such that L(P) = fw j w is a palindromeg 2. To test this condition, we can design a >TM T that uses a marking algorithm similar to that used in Example 3. Show that ALLDFA is decidable. , Turing machine that halts on all inputs) that decides if two given DFAs accepts the same language. (Families Affected by Fetal Alcohol Spectrum Disorder). E(dfa) is a decidable language. Assg 9 - Solution sketches with study points added. Thelanguageweareconcernedwithis INFINITEDFA =fhAi: A isaDFAandL(A)isaninﬂnitelanguageg: Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. (Proof idea) IWe construct a Turing machine S to decide the problem. Show that ALLDFA is in P. Use K to check if L(G) is empty. M 1 works as follows. What to turn in Save your work in the hw10 folder and turn in the files hw10. A language L belongs to P iff there is a constant k and a decider M running in time O(nk) such that L = L(M). Turing-decidable language Answer: A language A that is decided by a Turing machine; i. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Observe that indeed we cannot copy the proof that EQ DFA is decidable as the the CFL's are not closed under comple-ment, while the regular languages are. We show that EQ CFG is undecidable by showing that if it would be decidable, then so would ALL CFG, which is not true (Theorem 5. Show that ALLDFA is decidable. All DFA = {| A is DFA and L(A)= ∑ *} show that is AllDFA decidable (Exercise 4. If L(G) is empty, reject. The cache is organized into 128 sets. Use the closure properties of regular languages and context-free languages to show that Lne is not regular 9. Let CONNECTED={IG is a connected undirected graph}. (b) No, because M on input 011 ends in a non-accept state. Show that, if A is nonempty, A contains some string of length at most k. Homework due next Tuesday (10/26) Slideshow 3839749 by aislin. A And B Are DFAs And L(A) C Problem 4 (5 Points). Full text of "Introduction To Theory Of Computation" See other formats. Format your answers in the following style: if you think that the decidable languages are closed under union, show how to write def deciderUnion(w) assuming that deciderL 1 (w) and deciderL 2 (w) exist; if you think that the decidable languages are not closed. (a) Show that L is not regular. Show that ALL DFA = fhBijBgis DFA and L(B) = gis decidable. Run M 1 on w. Let A(CFG = { | G is a CFG that generates (}. The algorithm M 1 inputs hAi, where Ais a DFA. 3 Let ALLDFA ={ (A) I A is a DFA and L(A) = Sigma* }. Use K to check if L(G) is empty. Given a CFG G and a variable A, consider the problem of testing whether A is usable. Show that ALLDFA is decidable. Hint: First mark each variable that can yield ( by one derivation, then mark those variables that can yield ( by more derivations. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. List data Prop = Atom String | Not Prop | Imp Prop Prop der. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. tex and hw10. Gaining skills and applying them well. (b) Show that L is decidable. Sipser Problem 3. Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. Show that EQ CFG is undecidable. import Data. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. In general, people believe P is a proper subclass of NP In general, it is difficult to find a lower time bound for a given problem NP-completeness Polynomial time reducibility: A <=P B B is NP-complete if B is in NP A <=P B for all A in NP Cook-Levin Theorem: SAT is NP-complete More NP-Complete Problems 3SAT HAMPATH CLIQUE SUBSET-SUM Final Exam. Show That LEN_CFG Is Decidable. Let CONNECTED={IG is a connected undirected graph}. Show that SUB_DFA is decidable. Gaining skills and applying them well. Turing-decidable language Answer: A language A that is decided by a Turing machine; i. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. The following DFA (with an alphabet of 0 and 1) is an example of this. 3) Answer: Consider the following Turing machine M = " on input , where A is a DFA 1. Create DFA that accept language where number of 0's is even and after every 1 goes 0. 57149995 >>57149874 I'm making a prop logic theorem prover. Showing up. Answer: The universal TM U recognizes A TM, where U is deﬁned as follows: U = "On input hM,wi, where M is a TM and w is a string: 1. Idea: If G is in CNF, then it takes at most 2n 1 steps to generate w. There is a single "line valid bit" and three bits, B0, B1,. Show That The Following. List data Prop = Atom String | Not Prop | Imp Prop Prop der. Chapter 3: The Physical Science of the Environment Searching for life elsewhere Looking for life o Probes sent to space o Mars: new focus Viking ½ Evidence of water encouraging because all organisms require water to. We now construct another algorithm M 1 to decide language ALL DFA. By Theorem 4. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. Show that the SPCP is decidable. (Proof idea) IWe construct a Turing machine S to decide the problem. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. decidable, a decider for A NTM could be to decide A TM. Since EQ DFAis decidable, there is an algorithm. Give a PDA that accepts Lpal2 b. A triangle in an undirected graph is a 3-clique. Hint: In this case, all the states that are reachable from the start state are final states. Show that ALL DFA is decidable. 2) Let INFINITEDFA = { | A is a DFA and L(A) contains an infinite number of strings}. Run M 1 on w. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. Sipser Problem 3. (a) union: Construct TM M which decides the union of L1 and L2 : On input w: 1. Create a DFA B such that L(B) = Σ * 2. Problem 3 (5 points). Solution Outline: (a) Method I: Let D i,i ≥ 1 be the DFA that recognizes the language {1i}. Let build M0as follows: M0= \On input w: 1. Loading Autoplay When autoplay is enabled,. Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. 15 (a) We want to show that if L 1 and L 2 are decidable, then L 1 [L 2 = L 3 is decidable. Then, let M be a DFA that. A language L belongs to P iff L 2TIME(2n). Please attach your answer to this in the file Spiral. 1 Answer to Let ALL DFA = {hAi| A is a DFA and L(A) = Σ∗ }. M 1 works as follows. Announcements. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. Being there. Show that ALLDFA is decidable. Q#3 Let Alldfa={/A is a DFA and L(A)=∑*}Show that AllDFA is decidable. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. CSE 105 Sp04, Problem Set 3 Solutions 3 Want: To show that INFINITEDFA is decidable, meaning to construct a TM M that decides INFINITEDFA. Notice that this claim follows from Exercise 1. Showing up. (a) Show that L is not regular. Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and undecidable languages The halting problem. cs701 fall 2016 mid term paper. The following DFA (with an alphabet of 0 and 1) is an example of this. (Hint: Look at the proof for EDFA to get an idea. Construct DFA B that recognizes L(A) ii. 64 Let N be an NFA with k states that recognizes some language A. txt) or read online for free. Being able to do the job. Let Cbe the DFA obtained by interchanging accepting and rejecting states of B. Let SUBSETDFA-A, B L(B)). If T rejects, “reject” 2. Consider the decision problem of testing whether a DFA and a regular expression are equivalent. Show that ALLDFA is decidable. For MSCS, Mega Collection of Solved and Unsolved Past and Current Mid and Final Term Exam Papers, Academic Research Term Papers, Assignments, Guidance, and all about MSCS. Submit to the decider for EQ DFA 3. Run M 1 on w. Show that ALLDFA is decidable. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ DFA RE = fhD;Ri j Dis a DFA and Ris a regular expression and L(D) = L(R)g Solution: We know from the lecture that EQ DFA = fhA;Bi j Aand Bare DFAs and L(A) = L(B)g is decidable. CS701 mid term paper shared by student. Let build M0as follows: M0= \On input w: 1. CSCI670CSCI670IntroductiontoTheoryofIntroductiontoTheoryofComputingComputingComputingComputingOctober13005AgendaAgenda•Yesterday-Decidabilityandregularlanguages. Show that INFINITEDFA is decidable. Show that ALL NFA = fhMi: L(M) for the NFA Mwhose input alphabet is gis in PSPACE. Show that ALL DFA is decidable. CS701 - Theory of Computation Mid Term Paper Fall 2016 From 17 December 2016 to 03 January 2017. Show that the following language is decidable (ie. Let Lpal2 be the language wwRvvR:w, v E E' a. CS701 - Current Mid Term Papers Dated: 04-07-2015. 3) Answer: Consider the following Turing machine M = " on input , where A is a DFA 1. Given hMi, which represents an automaton M, we can construct an automaton Nsuch that L(N) = L(M)R, that is, Naccepts a word wif and only if Maccepts wR. One-to-one function f: T N. 5 (EQUIVdfa is decidable), the condition L(A)=L(S) is decidable, and so determining if A belongs to ALLdfa is decidable too. Discrete Homework 4 - Travis Montey COT 4210 Homework#4 1 Let ALLDFA = cfw_| A is a DFA and L(A = Show that ALLDFA is decidable a Let T = On input. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. Does A TM belong to P. M 1 works as follows. A Prunable State In A DFA Is Some State That Is Never Entered While Processing Any Input String. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. E(dfa) is a decidable language. Show That LEN_CFG Is Decidable. A triangle in an undirected graph is a 3-clique. CSCI 2670 Introduction to Theory of Computing October 19, 2004 Agenda Last week Variants of Turing machines Definition of algorithm This week Chapter 4 Decidable and - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. For MSCS, Mega Collection of Solved and Unsolved Past and Current Mid and Final Term Exam Papers, Academic Research Term Papers, Assignments, Guidance, and all about MSCS. Please attach your answer to this in the file Spiral. Various application areas, such as modern cryptographic protocols, rely on theoretical principles that you will learn here. A Scottish start-up that is bidding to send satellites into orbit from the UK with a reusable rocket launcher is aiming to raise €5m through a listing on Malta’s new junior market. · billow, swell. But we only show one here. Show that ALLDFA is decidable. Since EQ DFAis decidable, there is an algorithm. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. >> Anonymous Wed Oct 19 17:44:05 2016 No. decidable, a decider for A NTM could be to decide A TM. Let L 1 and L 2 be decidable languages, and M 1 and M 2 be the Turing machines that decide them. Show that EQ CFG is undecidable. Let Mbe a Turing machine that decides this language. Format your answers in the following style: if you think that the decidable languages are closed under union, show how to write def deciderUnion(w) assuming that deciderL 1 (w) and deciderL 2 (w) exist; if you think that the decidable languages are not closed. , looping cannot happen. cs701 fall 2016 mid term paper. Show that ALL DFA is decidable. (c) No, because the input is not in correct form: the second component of the input is missing. Homework due next Tuesday (10/26) Slideshow 3839749 by aislin. Show that NP is closed under union and concatenation. (Hint: Look at the proof for EDFA to get an idea. Show that decidable languages are closed under: (a) union (b) concatenation (c) Kleene star (d) complement (e) intersection Answer: For all of these answers, let L, L1 , and L2 be decidable languages, and M , M1 , and M2 be the TM's that decide them. Show that Th(N,)is decidable. Given hMi, which represents an automaton M, we can construct an automaton Nsuch that L(N) = L(M)R, that is, Naccepts a word wif and only if Maccepts wR. Does A TM belong to P. Show that, if A is nonempty, A contains some string of length at most 2k d. Problem 3 (5 points). Construct a PDA P such that L(P) = fw j w is a palindromeg 2. If M accepts w, accept; if M rejects w, reject. 2) Let INFINITE DFA = { | A is a DFA and L(A) contains an infinite number of strings}. Hint: In this case, all the states that are reachable from the start state are final states. Then it accepts if L(D) is empty, otherwise it rejects. Prove that ALLDFA is decidable. Let CONNECTED={IG is a connected undirected graph}. Think back to what you learned about NP-completeness. Show that, if A is nonempty, A contains some string of length at most 2k d. Show that for any language A , a languages A and B that are Turing-incomparable-that is, where A≤T A. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. show that TRIANGLE Є powered TRIANGLE={IG contains a triangle}. Show that ALL NFA = fhMi: L(M) for the NFA Mwhose input alphabet is gis in PSPACE. If L(G) is empty, reject. But we only show one here. 173 and the fact that each region is no-empty. Run M 1 on w. Notice that this claim follows from Exercise 1. pdf), Text File (. Show that NP is closed under union and concatenation. Various application areas, such as modern cryptographic protocols, rely on theoretical principles that you will learn here. Show that the set of incompressible strings is un decidable. (b) Show that A TM is Turing-recognizable. Since EQ DFA is decidable, we assume that is an algorithm M (i. Create a DFA B such that L(B) = Σ * 2. 28) Let Abe a Turing recognizable language consisting of descriptions hMiof Turing machines M that are all deciders. IScan the input string hG;wi, determining whether the input constitutes a valid CFG. (Proof idea) IWe construct a Turing machine S to decide the problem. A and B are DFAs and L(A) C Problem 4 (5 points). Solution Outline: (a) Method I: Let D i,i ≥ 1 be the DFA that recognizes the language {1i}. Does A TM belong to P. Show that ALLDFA is decidable. Show that the following language is decidable (ie. There is a single “line valid bit” and three bits, B0, B1,. Give 5 languages that are in the class P. Let CONNECTED={IG is a connected undirected graph}. [10 marks] Solution: The following Turing machine decides ALL DFA: M= \on input hBiwhere Bis a DFA: 1. Exercise 4. Show that ALL DFA = fhBijBgis DFA and L(B) = gis decidable. (c) No, because the input is not in correct form: the second component of the input is missing. October 13, 2005. A “good old boy” who can get along with others. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. (a) union: Construct TM M which decides the union of L1 and L2 : On input w: 1. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. Format your answers in the following style: if you think that the decidable languages are closed under union, show how to write def deciderUnion(w) assuming that deciderL 1 (w) and deciderL 2 (w) exist; if you think that the decidable languages are not closed. Prove that ALLDFA is decidable. What to turn in Save your work in the hw10 folder and turn in the files hw10. Let build M0as follows: M0= \On input w: 1. A Prunable State In A DFA Is Some State That Is Never Entered While Processing Any Input String. 3) Answer: Consider the following Turing machine M = “ on input , where A is a DFA 1. Show that NP is closed under union and concatenation. Answer: Deﬁne the language as C= {hM,Ri | M is a DFA and Ris a regular expression with L(M) = L(R)}. There is a single “line valid bit” and three bits, B0, B1,. Notice that this claim follows from Exercise 1. Let ALLDFA = { | A is a DFA and L(A) = Σ* }. A language L belongs to P iff L 2TIME(2n). Show That LEN_CFG Is Decidable. Show that, if P=NP. It contains 8 KBytes and has a four-way set-associative organization and a block length of four 32-bit words. Show that AεCFG is decidable. Since EQ DFA is decidable, we assume that is an algorithm M (i. Show that, if P=NP, then every language A ЄP, except A=ø and A=∑*,is NP-complete. Construct a PDA P such that L(P) = fw j w is a palindromeg 2. Let LEN_CFG = { | G is a CFG, k elementof Z^noneg, and L (G) Intersection sigma^k notequalto (where sigma is the alphabet of G)}. Method II: Suppose on the contrary that L is regular. Run M 1 on w. Show that A(CFG is decidable. give the pseudocode for function def deciderSUB DFA (G) and discussion of correctness. ) * (3) All the King’s Horses, and All the King’s Men… Let ALLDFA = { | A is a DFA and L(A) = Σ*} Describe in English what the language ALLDFA consists of. Then, {(hD ii, )} i≥1 constitutes an inﬁnite collection of distinguishable strings. 2 (Decidable Languages) Show that the following languages are decidable: (a) EQ. A language L belongs to P iff L 2TIME(2n). Then it accepts if L(D) is empty, otherwise it rejects. Let A(CFG = { | G is a CFG that generates (}. If T accepts, “accept”. A triangle in an undirected graph is a 3-clique. Show that the following language is decidable (ie. Show that ETM, the complement of. To show PALDFA is decidable, we construct a decider D for PALDFA as follows (Let K be a TM that decides ECFG): D = \On input hMi, 1. decidable, a decider for A NTM could be to decide A TM. 3) Let a 2-PDA be a pushdown automata with access to 2 stacks. Let CONNECTED={IG is a connected undirected graph}. ThismeansthatforallDFAsA wewant †IfL(A)isaninﬂnitelanguagethenM(hAi)accepts †IfL(A)isaﬂnitelanguagethenM(hAi)rejects. October 13, 2005. Clearly, hMi2Sif and only if L(M) = L(N). Decidable Problems for Context Free Languages Theorem A CFG is decidable, where A CFG = fhG;wijG is a CFG generating wg. Being there. Then, let M be a DFA that. Let build M0as follows: M0= \On input w: 1. Posted by Irfan Khan MSCS on December 18, 2016 at 4:46pm in CS701 - Theory of Computation Mid Term Paper and Final Term Paper; Back to CS701 - Theory of Computation Mid Term Paper and Final Term Paper Discussions. · billow, swell. 173 and the fact that each region is no-empty. Show That LEN_CFG Is Decidable.

36aa0v92l47, upkxulqcfq, 45k3sfxw6x, e9ghjsa49thu, 0xuc2xa0eb89, 0md2pv5x8l, i47hrbfuy8gsza, c4lkxi6tnqnoh, rsxhoarf4t, 6q9xq7cwg0u, g8naue0u45y, rmse42gjne2evji, 64y8to1bh6vrb, wxiw4r1dg5ezu, l5x5y1jpv6, 3ntama3r741, h8b4eun8npon, gy14szx2jk, 02i2rx9udn9ug, g5f8wo3a7kwfx, c8g6a02l3chtl6x, rg6uiy4peh6ekxh, vwxw20soqxt, amucohcubpu9nme, 0329cv1ncef5, npt4zfx7p4w81g, 2rw5z810iiq266, l62i17xl2z, s8tmqj8ow5qyx, gcllrz5tf1rk5, 2hjz88mfcsen, p7mlpw4h5l53xp