# The Emptiness Problem for Intersections of Regular Languages

@inproceedings{Lange1992TheEP, title={The Emptiness Problem for Intersections of Regular Languages}, author={Klaus-J{\"o}rn Lange and Peter Rossmanith}, booktitle={International Symposium on Mathematical Foundations of Computer Science}, year={1992} }

Given m finite automata, the emptiness of intersection problem is to determine whether there exists a string which is accepted by all m automata. In the following we consider the case, when m is bounded by a function in the input length, i.e., in the size and number of the automata. In this way we get complete problems for nondeterministic space-bounded and timespace-bounded complexity classes. Further on, we get close relations to nondeterministic sublinear time classes and to classes which…

## 36 Citations

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This work focuses on three types of problems: universality, equivalence, and emptiness of intersection, known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets.

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This work raises the issue of limiting the number of final states in the automata intersection problem, and considers idempotent commutative automata and group automata with one, two, or three final states over a singleton or larger alphabet, elucidating the complexity of the intersection nonemptiness and related problems in each case.

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A reduction technique is applied to show that if intersection non-emptiness for k tree shaped automata is solvable in no(k) time, then the exponential time hypothesis (ETH) is false, and a parameterized equivalence is introduced between intersection non -emptiness, weighted CNFSAT, and the clique problem for hypergraphs.

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The deterministic finite-state automata intersection problem is reduced to the problem of deciding co-observability for regular languages using a polynomial-time many-one mapping, demonstrating that the problem is PSPACE-complete and probably intractable.

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