The Hamiltonian Circuit Problem and Automaton Theory B. Litow Abstract We exhibit an elegant automaton-theoretic construction that yields a 2 (n)-time algorithm to count the number of Hamiltonian circuits in a graph with n vertices. We point out that a simple 2 (n) time algorithm for # H A M (counting the number of Hamiltonian circuits) can be obtained directly from basic a u t o m a t o n theory. The approach highlights the linear algebraic theory of automata. For example, see the book by Kuich and Salomaa [2]. The ring of integers is denoted by Z. The a u t o m a t o n definition that we use is due to Schiitzenberger. This definition can be generalized in several directions. A formal series is simply a mapping f ¢ E* ~ Z, so that for w E E*, f ( w ) E Z. If f ( w ) = 0 for all but finitely many w, f is called a formal polynomial. A finite automaton A with d states over Z is a tuple (E, U, V, M 1 , . . . , Mr), where E = { a l ,
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The Hamiltonian circuit problem and automaton theory
Litow, B.
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, Volume 34 (2)
Association for Computing Machinery – Jun 1, 2003
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