Minimization of fuzzy finite automata
Information Sciences: an International Journal
Model-checking infinite state-space systems with fine-grained abstractions using SPIN
SPIN '01 Proceedings of the 8th international SPIN workshop on Model checking of software
A framework for multi-valued reasoning over inconsistent viewpoints
ICSE '01 Proceedings of the 23rd International Conference on Software Engineering
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Model Checking Partial State Spaces with 3-Valued Temporal Logics
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Finite-state transducers in language and speech processing
Computational Linguistics
Ranking Automata and Games for Prioritized Requirements
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Handbook of Weighted Automata
From Boolean to quantitative notions of correctness
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Nondeterministic Moore automata and Brzozowski's minimization algorithm
Theoretical Computer Science
Approximating deterministic lattice automata
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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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 problem of minimization is open. In this paper we study minimization of lattice automata. We show that it is impossible to define a right congruence in the context of lattices, and that no canonical minimal automaton exists. Consequently, the minimization problem is much more complicated, and we prove that it is NP-complete. As good news, we show that while right congruence fails already for finite lattices that are fully ordered, for this setting we are able to combine a finite number of right congruences and generate a minimal deterministic automaton in polynomial time.