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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 the foundation that any computer scientist is expected to know. The study of computation intended for providing an insight into the characteristics of computations. Such an insight may be used for predicting the difficulty of desired computations, for selecting the approaches they should take, and for developing tools that facilitate their design. Study of computation also provides tools for identifying problems that can possibly be solved, as well as tools for designing such solutions that is the field of computer sciences deals with the development of methodologies for designing programs and with the development of computers for the implementation of programs.
The study of computability also develops precise and well-defined language for communicating perceptive thoughts about computations. It reveals that there are problems that cannot be solved. And of the problems that can be solved, there are some that require infeasible amount of resources (e.g., millions of years of computation time). These revelations might seem discouraging, but they have the benefit of warning against trying to solve such problems. The study of computation provides approaches for identifying such problems are also provided by the study of computation.
Computation should be studied through medium of programs because programs are descriptions of computations. The clear understanding of computation and programs requires clear discussion of the following concepts
• "Alphabets, Strings, and Representation • Formal languages and grammar• Programs• Problems• Reducibility among problems"
write short notes on decidable and solvable problem
Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
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
build a TM that enumerate even set of even length string over a
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1 and G2. The two grammars can be shown to
distinguish between histogram and historigram
We can then specify any language in the class of languages by specifying a particular automaton in the class of automata. We do that by specifying values for the parameters of the
We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
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