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We can then specify any language in the class of languages by specifying a particular automaton in the class of automata. We do that by specifying values for the parameters of the class. In this way, we can regard a specification of those parameters as a definition of a language in the class. Given our assumption of finiteness for the parameters, the definition will be finite.
The specification itself will be a mathematical object-a tuple of values, one for each parameter. We can illustrate this process by applying it to the class of Finite Languages. The obvious algorithm for recognizing such a language is to use a lookup table containing all and only the strings in the language. We then simply read the entire input and check to see if it is in the table. A schematic representation of an automaton implementing this algorithm is shown in Figure 1. The input is shown across the top, written on a tape one symbol per cell of the tape. (The structure of the input is irrelevant here, but will matter when we work with automata that scan the input sequentially.) The ∈ element, here, outputs TRUE iff its first input is a member of the set presented to its second input, so it represents some sort of search mechanism.
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
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examples of decidable problems
Computation of a DFA or NFA without ε-transitions An ID (q 1 ,w 1 ) computes (qn,wn) in A = (Q,Σ, T, q 0 , F) (in zero or more steps) if there is a sequence of IDs (q 1
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
phases of operational reaserch
The SL 2 languages are speci?ed with a set of 2-factors in Σ 2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and en
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat
The Last Stop Boutique is having a five-day sale. Each day, starting on Monday, the price will drop 10% of the previous day’s price. For example, if the original price of a product
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