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Various aspects of theory of computation
The theory of computation is that branch of theoretical computer science which deals with solving problems effectively using various models of computations. Algorithms are also used in theory of computation. The turing machine model is the most widely used model. The computer scientists find the turing machines easy to use, analyze and reasonable. This makes the turing machine the most affective model of computation using a finite amount of memory.
Theory of computation is now a separate disciple of academics, which is separate from mathematics. Some great name associated with theory of computation is Stephen Kleene, Claud Shannon, Noam Chomsky, and Alonzo Church etc.
There are various braches of theory of computation
Automata theory deals with the abstract mathematical machines and systems, and the computational problems they solve. The automata theory is also closely related to the language theory and can be finite representation of infinite set of formal language.
Computability theory determines to what extent a problem can be solved on computer. This is the main focus of the computability theory. Computability theory proved that halting problems could not be solved by Turing machine. Computability theory also gave the rice theorem which states that it is not decidable that a Turing machine computes and solves a partial function with non trivial qualities. and property. Computability theory relates to the recursion theory’s mathematical logic. Thus, other models, which are not reducible to Turing model, can also be studied. Many computational theorists and mathematicians also refer to recursion theory as computability theory, because of the similarities.
Computational complexity theory deals with the effectiveness of problem solving. Based on time and space complexity, it determines the number of steps and memory required to perform a computation.
Various models of computation
The other models in use (besides Turing machine) are as follows:
Lambda calculus-the computation has an initial lambda expression (two for separate input and function) and a finite sequence of lambda terms. The terms are obtained from the preceding terms by beta reduction application.
Combinatory logic-it is similar to the lambda calculus with a few dissimilarities for example the combinator y is in normal form in combinatory logic as compared to lambda logic. Combinatory logic makes the mathematical foundations and the nature of paradoxes simpler and eliminates variable notions.
Mu recursive functions-It has a defining sequence of input and output functions. The final term gives the value of the recursive functions which was originally applied to the inputs. The mu recursive functions are the exact functions to be computed by the Turing machine. They return a single natural number from the tuples of natural numbers that are inputted.
Markov algorithm-The rules of this algorithm are grammar like and it operates on strings of symbols. It is basically a rewriting system which was invented by mathematician Andrei Andreevich Markov.Jr in 1960.the Markov algorithm contains set of productions and alphabets.
Register machine- is the idealization of computer. Every register can hold a natural number of any size. The method is simple to use and uses Godal numbering techniques. Unambuiguity in interpretation and representation is maintained by number theoretical foundations.
Some special and restricted applications are used in simpler computational models, which also are there in addition to general computational models. Spring patterns in many contexts are specified by regular expressions. These range form programming languages to office productivity software’s. The regular expression equivalent finite automata, is used in problem solving and circuit design in computational problems. Equivalents of context free grammar such as pushdown automata are present.
Different coDifferent computational theory models help in undertaking different tasks and solving problems of different kinds and proportions. The more class of languages a computational model can generate the more important and powerful it is.
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