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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.
The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p
designing DFA
These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third
implementation of operator precedence grammer
All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat
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
Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as the
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
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
Construct a Moore machine to convert a binary string of radix 4.
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