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Write implememnt a finite state machine that recognzes an input string according to the following rules.
1. The first character must be either a letter(upper or lower case.)2. Each subsequent character can be an letter or any digit.3.Each string mus contain at least one lowercase letter, at least one uppercaseletter, and at least one digit.
Express the following set as a regular expression: The set of all strings of length at least three over {0,1} such that every three consecutive.
Show that the language F = {a^i b^j c^k | i, j, k greater than or equal to 0 and if i = 1 then j = k} is not regular. Show, however, that it satisfies the statement of the pumping lemma
Design Turing machine (using Sipser notation) having at least 4 nontrivial (i.e., nonrejecting) states and at least six nontrivial (i.e., not to the rejecting state) transitions.
Prove that L is not regular. (Be particularly careful if you use the Pumping Theorem. You must choose a w that is actually in L.)
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
Show that the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
Write a grammar for the language consisting of strings that have n copies of the letter a followed by same number of copies of the letter b, where n>0
Express the given correctness properties in LTL. Defne propositions/variables to model the events mentioned in the question. If a parent process calls the blocking waitpid() system call then it is blocked until child process terminates.
Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
Given monotone instance of Satisfiability, together with number k, problem of Monotone Satisfiability with Few True Variables asks: is there satisfying assignment for instance in which at most k variables are set to 1.
How the problem would be encountered in attempting to represent the following statements in Predicate logic. it should be possible to: John only likes to see French movies.
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