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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"
First model: Computer has a ?xed number of bits of storage. You will model this by limiting your program to a single ?xed-precision unsigned integer variable, e.g., a single one-by
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
The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive
s-> AACD A-> aAb/e C->aC/a D-> aDa/bDb/e
write short notes on decidable and solvable problem
LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl
Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
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
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode
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