Transition graphs, Theory of Computation

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled ‘?') and the edges were labeled with individual alphabet symbols. The k-factors of the automaton could be recovered by appending the symbol on an edge to the factor of the node it is incident from. The key value of the graphs is the way that they capture the set of all computations of the automaton in a concise form: every computation of the automaton corresponds to a path through the automaton from ‘?' to ‘?' and vice versa. The su?x substitution closure property is, in essence, a consequence of this fact. All that is signi?cant about the initial portion of a computation is the node it ends on. All strings that lead to the same node are equivalent in the sense that any continuation that extends one of them to form a string that is accepted will extend any of them to form a string that is accepted, and any continuation that leads one of them to be rejected will lead any of them to be rejected.

In adapting this idea for LTk automata, we have to confront the fact that the last k - 1 symbols of the input are no longer enough to characterize the initial portion of a string. We now will also need the record of all k-factors which occurred in that initial portion. To accommodate this, we will extend the labeling of our nodes to include sets of k-factors. The node set will be pairs in which the ?rst component is a k - 1 factor (the last k - 1 symbols of the input) and the second component is a set of k-factors. At the initial node, not having scanned any of the input yet, we have seen no k-factors, that is, the initial set of k-factors is empty (∅). The label of the initial node, then is (?, ∅).

Posted Date: 3/21/2013 3:21:04 AM | Location : United States







Related Discussions:- Transition graphs, Assignment Help, Ask Question on Transition graphs, Get Answer, Expert's Help, Transition graphs Discussions

Write discussion on Transition graphs
Your posts are moderated
Related Questions
how to write program Minimum Cost Calculation - Vogel Approximation Method(VAM

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled

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


These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third

Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}

Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th

The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea

A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note

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