An introduction to parallel algorithms
An introduction to parallel algorithms
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Communications of the ACM
SIAM Journal on Computing
Algorithms for Computing Small NFAs
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
FA Minimisation Heuristics for a Class of Finite Languages
WIA '99 Revised Papers from the 4th International Workshop on Automata Implementation
Rewriting Regular Inequalities (Extended Abstract)
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
On the State Minimization of Nondeterministic Finite Automata
IEEE Transactions on Computers
Incremental construction of minimal acyclic finite state automata and transducers
FSMNLP '09 Proceedings of the International Workshop on Finite State Methods in Natural Language Processing
Fuzzy relation equations and reduction of fuzzy automata
Journal of Computer and System Sciences
Reducing the size of NFAs by using equivalences and preorders
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Minimizing NFA's and regular expressions
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Construction of fuzzy automata from fuzzy regular expressions
Fuzzy Sets and Systems
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We present different techniques for reducing the number of states and transitions in nondeterministic automata. These techniques are based on the two preorders over the set of states, related to the inclusion of left and right languages. Since their exact computation is NP-hard, we focus on polynomial approximations which enable a reduction of the NFA all the same. Our main algorithm relies on a first approximation, which can be easily implemented by means of matrix products with an O(sn4) time complexity, and optimized to an O(sn3) time complexity, where s is the average nondeterministic arity and n is the number of states. This first algorithm appears to be more efficient than the known techniques based on equivalence relations as described by Lucian Ilie and Sheng Yu. Afterwards, we briefly describe some more accurate approximations and the exact (but exponential) calculation of these preorders by means of determinization.