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
De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p

Another striking aspect of LTk transition graphs is that they are generally extremely ine?cient. All we really care about is whether a path through the graph leads to an accepting

We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea

Strictly 2-local automata are based on lookup tables that are sets of 2-factors, the pairs of adjacent symbols which are permitted to occur in a word. To generalize, we extend the

Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh

Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev

Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second

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

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

De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where