Nondeterministic space is closed under complementation
SIAM Journal on Computing
The minimum consistent DFA problem cannot be approximated within any polynomial
Journal of the ACM (JACM)
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
Approximate recognition of non-regular languages by finite automata
ACSC '05 Proceedings of the Twenty-eighth Australasian conference on Computer Science - Volume 38
Ranking Automata and Games for Prioritized Requirements
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Handbook of Weighted Automata
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Minimizing deterministic lattice automata
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Formal analysis of online algorithms
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
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Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0,1,…,n−1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have interesting theoretical properties as well as applications in formal methods. Minimal deterministic automata capture the combinatorial nature and complexity of a formal language. Deterministic automata have many applications in practice. In [13], we studied minimization of deterministic lattice automata. We proved that the problem is in general NP-complete, yet can be solved in polynomial time in the case the lattices are fully-ordered. The multi-valued setting makes it possible to combine reasoning about lattice automata with approximation. An approximating automaton may map a word to a range of values that are close enough, under some pre-defined distance metric, to its exact value. We study the problem of finding minimal approximating deterministic lattice automata defined with respect to fully-ordered lattices. We consider approximation by absolute distance, where an exact value x can be mapped to values in the range [x−t,x+t], for an approximation factor t, as well as approximation by separation, where values are mapped into t classes. We prove that in both cases the problem is in general NP-complete, but point to special cases that can be solved in polynomial time.