Semirings, automata, languages
Semirings, automata, languages
Three partition refinement algorithms
SIAM Journal on Computing
Rational series and their languages
Rational series and their languages
CCS expressions finite state processes, and three problems of equivalence
Information and Computation
Equality relations as a basis for fuzzy control
Fuzzy Sets and Systems
SIAM Journal on Computing
Forward and backward simulations I.: untimed systems
Information and Computation
Handbook of formal languages, vol. 1
Minimization of fuzzy finite automata
Information Sciences: an International Journal
Communicating and mobile systems: the &pgr;-calculus
Communicating and mobile systems: the &pgr;-calculus
Towards a unified view of bisimulation: a comparative study
Theoretical Computer Science
Finite nondeterministic automata: simulation and minimality
Theoretical Computer Science
Fuzzy points, fuzzy relations and fuzzy functions
Discovering the world with fuzzy logic
Communication and Concurrency
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
On quotient machines of a fuzzy automaton and the minimal machine
Fuzzy Sets and Systems
Algorithms for Computing Small NFAs
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Computing the Equation Automaton of a Regular Expression in Space and Time
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Constructing NFA s by Optimal Use of Positions in Regular Expressions
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Reducing NFAs by invariant equivalences
Theoretical Computer Science
From Bisimulation to Simulation: Coarsest Partition Problems
Journal of Automated Reasoning
Information and Computation
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
NFA reduction algorithms by means of regular inequalities
Theoretical Computer Science - Developments in language theory
Theoretical Computer Science - Insightful theory
Minimization of states in automata theory based on finite lattice-ordered monoids
Information Sciences: an International Journal
Fuzzy equivalence relations and their equivalence classes
Fuzzy Sets and Systems
Equivalence in automata theory based on complete residuated lattice-valued logic
Fuzzy Sets and Systems
Determinization of fuzzy automata with membership values in complete residuated lattices
Information Sciences: an International Journal
On the State Minimization of Nondeterministic Finite Automata
IEEE Transactions on Computers
Bisimulation relations for weighted automata
Theoretical Computer Science
Generalizing the Paige--Tarjan algorithm by abstract interpretation
Information and Computation
Uniform fuzzy relations and fuzzy functions
Fuzzy Sets and Systems
Automata theory based on complete residuated lattice-valued logic: Pushdown automata
Fuzzy Sets and Systems
Automata theory based on complete residuated lattice-valued logic: A categorical approach
Fuzzy Sets and Systems
Backward and forward bisimulation minimization of tree automata
Theoretical Computer Science
Congruences and homomorphisms of fuzzy automata
Fuzzy Sets and Systems
Myhill--Nerode type theory for fuzzy languages and automata
Fuzzy Sets and Systems
NFA reduction algorithms by means of regular inequalities
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Backward and forward bisimulation minimisation of tree automata
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Reducing the size of NFAs by using equivalences and preorders
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Factorization of fuzzy automata
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Bisimulations for fuzzy automata
Fuzzy Sets and Systems
Construction of fuzzy automata from fuzzy regular expressions
Fuzzy Sets and Systems
Weakly linear systems of fuzzy relation inequalities: The heterogeneous case
Fuzzy Sets and Systems
Computation of the greatest simulations and bisimulations between fuzzy automata
Fuzzy Sets and Systems
Fuzzy relation equations and subsystems of fuzzy transition systems
Knowledge-Based Systems
Nondeterministic automata: Equivalence, bisimulations, and uniform relations
Information Sciences: an International Journal
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We show that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states. This system may consist of infinitely many equations, and finding its non-trivial solutions may be a very difficult task. For that reason we aim our attention to some instances of this system which consist of finitely many equations and are easier to solve. First, we study right invariant fuzzy equivalences, and their duals, the left invariant ones. We prove that each fuzzy automaton possesses the greatest right (resp. left) invariant fuzzy equivalence, which provides the best reduction by means of fuzzy equivalences of this type, and we give an effective procedure for computing this fuzzy equivalence, which works if the underlying structure of truth values is a locally finite residuated lattice. Moreover, we show that even better reductions can be achieved alternating reductions by means of right and left invariant fuzzy equivalences. We also study strongly right and left invariant fuzzy equivalences, which give worse reductions than right and left invariant ones, but whose computing is much easier. We give an effective procedure for computing the greatest strongly right (resp. left) invariant fuzzy equivalence, which is applicable to fuzzy automata over an arbitrary complete residuated lattice.