First model of computation, Theory of Computation

Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explicit instruction to clear.) Limit your program to a single unsigned integer variable, and limit your methods of accessing it to something like inc(i), dec(i) and a predicate zero?(i) which returns true i? i = 0. This integer has unbounded precision-it can range over the entire set of natural numbers-so you never have to worry about your counter over?owing. It is, however, restricted to only the natural numbers-it cannot go negative, so you cannot decrement past zero.

(a) Sketch an algorithm to recognize the language: {aibi| i ≥ 0}. This is the set of strings consisting of zero or more ‘a's followed by exactly the same number of ‘b's.

(b) Can you do this within the ?rst model of computation? Either sketch an algorithm to do it, or make an informal argument thatit can't be  done.

(c) Give an informal argument that one can't recognize the language: {aibici| i ≥ 0} within this second model of computation (i.e, with
a single counter)

Posted Date: 3/20/2013 6:13:41 AM | Location : United States







Related Discussions:- First model of computation, Assignment Help, Ask Question on First model of computation, Get Answer, Expert's Help, First model of computation Discussions

Write discussion on First model of computation
Your posts are moderated
Related Questions
Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}

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


Question 2 (10 pt): In this question we look at an extension to DFAs. A composable-reset DFA (CR-DFA) is a five-tuple, (Q,S,d,q0,F) where: – Q is the set of states, – S is the alph

State and Prove the Arden's theorem for Regular Expression

(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?

Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi

The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan

A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove