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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"
Exercise: Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.
We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.
Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
what problems are tackled under numerical integration
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The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where
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