Transition and path functions, Theory of Computation

Assignment Help:

When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one state p such that hq, p, σi ∈ T. This function is called the transition function of the automaton and is usually denoted δ:

990_Transition and Path Functions.png

For any state q and symbol σ, then, δ(q, σ) is the state reached from q by following a single edge labeled σ. This can be extended to the path function, a function taking a state q and any string w ∈ Σ∗ which returns the statereached from q by following a path labeled w:

1907_Transition and Path Functions1.png

Note that ˆ δ is total (has some value for all q and w) and functional (that value is unique) as a consequence of the fact that δ is, which, in turn, is a consequence of the fact that the automaton is deterministic. In terms of the transition graph, this means that for any string w and any node q, there will always be exactly one path labeled w from q (which leads to δ(q,w)) and this is a consequence of the fact that there is always exactly one edge labeled σ from each node q of the graph and every σ ∈ Σ (which leads to δ(q, σ)).


Related Discussions:- Transition and path functions

Production, How useful is production function in production planning?

How useful is production function in production planning?

Theory of computation, Computations are deliberate for processing informati...

Computations are deliberate for processing information. Computability theory was discovered in the 1930s, and extended in the 1950s and 1960s. Its basic ideas have become part of

Give the acyclic paths through your graph, Give the Myhill graph of your au...

Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima

Turing machine, Design a turing machine to compute x + y (x,y > 0) with x a...

Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)

Assignment, Consider a water bottle vending machine as a finite–state autom...

Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as the

Strictly 2-local languages, The fundamental idea of strictly local language...

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

Formal languages and grammar, The universe of strings is a very useful medi...

The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie

Differentiate between dfa and nfa, Differentiate between DFA and NFA. Conve...

Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.

Universality problem, The Universality Problem is the dual of the emptiness...

The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd