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Technical Perspective: The Equivalence Problem For Finite Automata

By Thomas A. Henzinger, Jean-François Raskin

Communications of the ACM, Vol. 58 No. 2, Page 86

Formal languages and automata are fundamental concepts in computer science. Pushdown automata form the theoretical basis for the parsing of programming languages. Finite automata provide natural data structures for manipulating infinite sets of values that are encoded by strings and generated by regular operations (concatenation, union, repetition). They provide elegant solutions in a wide variety of applications, including the design of sequential circuits, the modeling of protocols, natural language processing, and decision procedures for logical formalisms (remember the fundamental contributions by Rabin, Büchi, and many others).

Much of the power and elegance of automata comes from the natural ease with which they accommodate nondeterminism. The fundamental concept of nondeterminism—the ability of a computational engine to guess a path to a solution and then verify it—lies at the very heart of theoretical computer science. For finite automata, Rabin and Scott (1959) showed that nondeterminism does not add computational power, because every nondeterministic finite automaton (NFA) can be converted to an equivalent deterministic finite automaton (DFA) using the subset construction. However, since the subset construction may increase the number of automaton states exponentially, even simple problems about determistic automata can become computationally difficult to solve if nondeterminism is involved.


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