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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.
Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is
A context free grammar G = (N, Σ, P, S) is in binary form if for all productions A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in bi
Application of the general suffix substitution closure theorem is slightly more complicated than application of the specific k-local versions. In the specific versions, all we had
Prove xy+yz+ýz=xy+z
how to prove he extended transition function is derived from part 2 and 3
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The Emptiness Problem is the problem of deciding if a given regular language is empty (= ∅). Theorem 4 (Emptiness) The Emptiness Problem for Regular Languages is decidable. P
We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1
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