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The SL2 languages are speci?ed with a set of 2-factors in Σ2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and end of the string, respectively), the recognizable languages are speci?ed with triples in Q × Q × Σ (along with an indication of the start and accepting states). In studying the SL languages, it was useful to consider those factors as tiles, allowing us to generate strings in the language recognized by the SL-automaton by laying them out in overlapping sequences. We can develop a similar generator model from our FSAs by extending the triples of the edge relation with triples from {?}×Q×{?} (to designate starting tiles)
We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1
Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?
De?nition Deterministic Finite State Automaton: For any state set Q and alphabet Σ, both ?nite, a ?nite state automaton (FSA) over Q and Σ is a ?ve-tuple (Q,Σ, T, q 0 , F), w
Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w
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
1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
In general non-determinism, by introducing a degree of parallelism, may increase the accepting power of a model of computation. But if we subject NFAs to the same sort of analysis
Computation of a DFA or NFA without ε-transitions An ID (q 1 ,w 1 ) computes (qn,wn) in A = (Q,Σ, T, q 0 , F) (in zero or more steps) if there is a sequence of IDs (q 1
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