Minimizing Deterministic Lattice Automata

Traditional automata accept or reject their input, and are therefore Boolean. In contrast, weighted automata map each word to a value from a semiring over a large domain. The special case of lattice automata, in which the semiring is a finite lattice, has interesting theoretical properties as well as applications in formal methods. A minimal deterministic automaton captures the combinatoric nature and complexity of a formal language. Deterministic automata are used in run-time monitoring, pattern recognition, and modeling systems. Thus, the minimization problem for deterministic automata is of great interest, both theoretically and in practice. For traditional automata on finite words, a minimization algorithm, based on the Myhill-Nerode right congruence on the set of words, generates in polynomial time a canonical minimal deterministic automaton. A polynomial algorithm is known also for weighted automata over the tropical semiring. For general deterministic weighted automata, the pr...

• Type: Journal
• Year: 2011
• Where: FOSSACS
• Authors: Shulamit Halamish, Orna Kupferman
• Keywords: Deterministic Automaton, FOSSACS 2011, Minimal Automaton, Polynomial Algorithm, Software Engineering