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Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about how to do this. For this claim the assumption that the solution of each instance is unique is not necessary; but both of the others are. If you had a program that checks whether a proposed solution to an instance of a problem is correct and another that systematically generates every instance of the problem along with every possible solution, how could you use them (as subroutines) to build a program that, when given an instance, was guaranteed to ?nd a correct solution to that problem under the assumption that such a solution always exists?
a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le
Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
#Your company has 25 licenses for a computer program, but you discover that it has been copied onto 80 computers. You informed your supervisor, but he/she is not willing to take an
While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica
Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua
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