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

Strictly local languages, While the SL 2 languages include some surprising...

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

Ogdens lemma, proof ogdens lemma .with example i am not able to undestand ...

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

Automata and compiler, Automata and Compiler (1) [25 marks] Let N be the...

Automata and Compiler (1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last f

Complement - operations on languages, The fact that SL 2 is closed under i...

The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that

Two-tape turing machine, Let there L1 and L2 . We show that L1 ∩ L2 is CFG ...

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

Fsa as generators, The SL 2 languages are speci?ed with a set of 2-factors...

The SL 2 languages are speci?ed with a set of 2-factors in Σ 2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and en

Pendulum Swings, how many pendulum swings will it take to walk across the c...

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

Suffix substitution closure, Our primary concern is to obtain a clear chara...

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

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