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When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable programming languages are equivalent in their power. Rather, we want to know if there is an algorithm for solving it that can be expressed in any rigorous way at all. Similarly, we are not asking about whether the problem can be solved on any particular computer, but whether it can be solved by any computing mechanism, including a human using a pencil and paper (even a limitless supply of paper).
What we need is an abstract model of computation that we can treat in a rigorous mathematical way. We'll start with the obvious model:
Here a computer receives some input (an instance of a problem), has some computing mechanism, and produces some output (the solution of that instance). We will refer to the con?guration of the computing mechanism at a given point in it's processing as its internal state. Note that in this model the computer is not a general purpose device: it solves some speci?c problem. Rather, we consider a general purpose computer and a program to both be part of a single machine. The program, in essence, specializes the computer to solve a particular problem.
Define the following concept with an example: a. Ambiguity in CFG b. Push-Down Automata c. Turing Machine
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Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici
The upper string r ∈ Q+ is the sequence of states visited by the automaton as it scans the lower string w ∈ Σ*. We will refer to this string over Q as the run of A on w. The automa
1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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