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Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, different interpretations that can be given to information. However, from the perspective of their power to express computations, there is very minute difference among them. Accordingly different programming languages can be used in the study of programs. The study of programs can benefit, however, from fixing the programming language in use. This enables a unified discussion about programs. So the program can be defined as a finite sequence of instructions over some domain D. The domain D, called the domain of the variables, is assumed to be a set of elements with a distinguished element, called the initial value of the variables. Each of the elements in D is assumed to be a possible assignment of a value to the variables of the program. The sequence of instructions is assumed to consist of instructions of the following form.
Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ 1 σ 2 ....... σ k-1 σ k asserts, in essence, that if we hav
This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But
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
This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.
Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to
Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
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write short notes on decidable and solvable problem
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
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
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