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Explain why every nonempty propositional clause, by itself, is satisfiable. Prove rigorously that every set of five 3-SAT clause is satisfiable, provided that each clause mentions exactly three distinct variables. What is the smallest set of such clauses that is unsatisfiable? Construct such a set.
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.
Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.
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.)
Design in JFLAP a Truing machine that takes as input a tape containing a series of n 1s, Where n >= 0, terminated by an = sign.
Give a construction that assumes you are given a DFA for L and show how to construct an NFA (with or without ε-moves) to recognize sort(L).
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.
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.
Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: n ≥ 0}. Write the first four strings in the lexicographic enumeration of L?
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
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
In this problem, we consider a very restricted subset of Boolean expressions. Define an operator to be one of the four symbols: ¬, ∧, ∨, and →. Define a variable to be one of the five symbols
Write down a structural induction principle for the PlayTree free type
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