Sign In

Communications of the ACM

Research highlights

Technical Perspective: The Equivalence Problem For Finite Automata

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.


No entries found

Log in to Read the Full Article

Sign In

Sign in using your ACM Web Account username and password to access premium content if you are an ACM member, Communications subscriber or Digital Library subscriber.

Need Access?

Please select one of the options below for access to premium content and features.

Create a Web Account

If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.

Join the ACM

Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.

Subscribe to Communications of the ACM Magazine

Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.

Purchase the Article

Non-members can purchase this article or a copy of the magazine in which it appears.
Sign In for Full Access
» Forgot Password? » Create an ACM Web Account