Positiveness problem - decision problems, Theory of Computation

For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable.

"Positiveness Problem".

Note that each instance of the Positiveness Problem is a regular language. (Each instance itself is, not the set of solved instances.) Clearly, we cannot take the set of strings in the language to be our instance, (since, in general, this is likely to be in?nite in size. But we have at least two means of specifying any regular language using ?nite objects: we can give a Finite State Automaton that recognizes the language as a ?ve-tuple, each component of which is ?nite, (or, equivalently, the transition graph in some other form) or we can give a regular expression. Since we have algorithms for converting back and forth between these two forms, we can choose whichever is convenient for us. In this case, lets assume we are given the ?ve-tuple. Since we have an algorithm for converting NFAs to DFAs as well, we can also assume, without loss of generality, that the automaton is a DFA.

A solution to the Positiveness Problem is just "True" or "False". It is a decision problem a problem of deciding whether the given instance exhibits a particular property. (We are familiar with this sort of problem. They are just our "checking problems"-all our automata are models of algorithms for decision problems.) So the Positiveness Problem, then, is just the problem of identifying the set of Finite State Automata that do not accept the empty string. Note that we are not asking if this set is regular, although we could. (What do you think the answer would be?) We are asking if there is any algorithm at all for solving it.

Posted Date: 3/21/2013 1:47:59 AM | Location : United States

Related Discussions:- Positiveness problem - decision problems, Assignment Help, Ask Question on Positiveness problem - decision problems, Get Answer, Expert's Help, Positiveness problem - decision problems Discussions

Write discussion on Positiveness problem - decision problems
Your posts are moderated
Related Questions
design a turing machine that accepts the language which consists of even number of zero''s and even number of one''s?

how many pendulum swings will it take to walk across the classroom?

#can you solve a problem of palindrome using turing machine with explanation and diagrams?

examples of decidable problems

Kleene called this the Synthesis theorem because his (and your) proof gives an effective procedure for synthesizing an automaton that recognizes the language denoted by any given r

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .

Construct a PDA that accepts { x#y | x, y in {a, b}* such that x ? y and xi = yi for some i, 1 = i = min(|x|, |y|) }. For your PDA to work correctly it will need to be non-determin

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