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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.
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
Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second
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
how to prove he extended transition function is derived from part 2 and 3
1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage 2. Prove the following language is non-Turing recognizable using the diagnolization
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construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.
One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part
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