1 The Foundations: Logic And Proofs 2 Basic Structures: Sets, Functions, Sequences, Sums, And Matrices 3 Algorithms 4 Number Theory And Cryptography 5 Induction And Recursion 6 Counting 7 Discrete Probability 8 Advanced Counting Techniques 9 Relations 10 Graphs 11 Trees 12 Boolean Algebra 13 Modeling Computation A Appendices expand_more
13.1 Languages And Grammars 13.2 Finite-state Machines With Output 13.3 Finite-state Machines With No Output 13.4 Language Recognition 13.5 Turing Machines Chapter Questions expand_more
Problem 1E: Describe in words the strings in each of these regular sets. a) 1*0 b) 1*00 c) 111001 d) (100)* e) (... Problem 2E Problem 3E Problem 4E Problem 5E: Express each of these sets using a regular expression. a) the set consisting of the strings 0, 11,... Problem 6E: Express each of these sets using a regular expression. a) the set containing all strings with zero,... Problem 7E: Express each of these sets using a regular expression. a) the set of strings of one or more 0s... Problem 8E: Construct deterministic finite-state automata that recognize each of these sets from I*, where l is... Problem 9E: Construct nondeterministic finite-state automata that recognize each of the sets in Exercise 8. 8.... Problem 10E: Construct nondeterministic finite-state automata that recognize each of these sets. a) ,0 b) 0,11 c)... Problem 11E: Show that if A is a regular set, then AR, the set of all reversals of strings in A, is also regular. Problem 12E: Using the construction described in the proof of Keene's theorem, find nondeterministic finite-state... Problem 13E: Using the construction described in the proof of Keene's theorem, find nondeterministic finite-state... Problem 14E: Construct a nondeterministic finite-state automaton that recognizes the language generated by the... Problem 15E: In Exercises 15-17 conflict a regular grammar G=(V,T,S,P) that generates the language recognized by... Problem 16E: In Exercises 15-17 conflict a regular grammar G=(V,T,S,P) that generates the language recognized by... Problem 17E: In Exercises 15-17 conflict a regular grammar G=(V,T,S,P) that generates the language recognized by... Problem 18E: Show that the finite-state automaton constructed from a regular grammar in the proof of Theorem 2... Problem 19E: Show that the regular grammar constructed from a finite-state automaton in the proof of Theorem 2... Problem 20E: Show that every nondeterministic finite-state automaton is equivalent to another such automaton that... Problem 21E: Let M=(S,I,f,s0,F) be a deterministic finite-state automaton. Show that the language recognized by... Problem 22E: One important technique used to prove that certain sets not regular is the pumping lemma. The... Problem 23E: Show that the set 02n1nn=0,1,2,... is not regular using the pumping lemma given in Exercise 22. *22.... Problem 24E: Show that the set {1n2n=0,1,2,...} is not regular using the pumping lemma given in Exercise 22. *22.... Problem 25E: Show that the set of palindromes over {0, 1} is not regular using the pumping lemma given in... Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E: Use Exercise 29 to show that the language consisting of all bit strings that are palindromes (that... format_list_bulleted