The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Polynomial space counting problems
SIAM Journal on Computing
Intersection and union of regular languages and state complexity
Information Processing Letters
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
The parallel complexity of finite-state automata problems
Information and Computation
SIAM Journal on Computing
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Hyper-minimisation Made Efficient
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
An nlogn algorithm for hyper-minimizing a (minimized) deterministic automaton
Theoretical Computer Science
On minimising automata with errors
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Finding lower bounds for nondeterministic state complexity is hard
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Brzozowski's minimization algorithm: more robust than expected
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Hyper-optimization for deterministic tree automata
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Minimization of symbolic automata
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We introduce E-equivalence, which is a straightforward generalization of almost-equivalence. While almost-equivalence asks for ordinary equivalence up to a finite number of exceptions, in E-equivalence these exceptions or errors must belong to a (regular) set E. The computational complexity of minimization problems and their variants w.r.t. almost- and E-equivalence are studied. Roughly speaking, whenever nondeterministic finite automata (NFAs) are involved, most minimization problems, and their equivalence problems they are based on, become PSPACE-complete, while for deterministic finite automata (DFAs) the situation is more subtle. For instance, hyper-minimizing DFAs is NL-complete, but E-minimizing DFA s is NP-complete, even for finite E. The obtained results nicely fit to the known ones on ordinary minimization for finite automata. Moreover, since hyper-minimal and E-minimal automata are not necessarily unique (up to isomorphism as for minimal DFAs), we consider the problem of counting the number of these minimal automata. It turns out that counting hyper-minimal DFAs can be done in FP, while counting E-minimal DFA s is #P-hard, and belongs to the counting class #·coNP.