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… 

Problems on Finite Automata and the Exponential Time Hypothesis

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.

The complexity of intersecting finite automata having few final states

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.

On the Complexity of Intersection Non-emptiness for Star-Free Language Classes

A family of languages is identified that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs, the first superpolynomial separation between these two models of computation.

On Computational Complexity of Set Automata

It was shown that DSA-languages look similar to DCFL due to their closure properties and NSA-l languages lookSimilar to CFLdue to their undecidability properties.

Intersection Non-Emptiness for Tree Shaped Finite Automata

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.

On the Complexity of Intersecting Regular, Context-Free, and Tree Languages

A construction of Cook 1971 is applied to show that the intersection non-emptiness problem for one PDA pushdown automaton and a finite list of DFA's deterministic finite automata characterizes the complexity class P, and constants c_1 and c_2 are shown to be solvable in time.

Finite Automata Algorithms in Map-Reduce

A lower bound on replication rate for computing NFA intersections is derived and three concrete algorithms for the problem are provided and investigated, showing where each algorithm could be applied through detailed experiments on large datasets of finite automata.

The Intersection Problem for Finite Monoids

We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there

Deciding co-observability is PSPACE-complete

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.

Descriptional and Computational Complexity of Finite Automata

This paper tours a fragment of a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept and discusses developments relevant to finite Automata related problems like, for example, simulation of and by several types of infinite automata.

References

SHOWING 1-10 OF 20 REFERENCES

Computational Calculus and Hardest Languages of Automata with Abstract Storages

Some hardest languages for classes of languages accepted by some automata with storages are given, showing a close relationship between the word problem of two- way automata and the emptiness problem of one-way automata.

Word problems requiring exponential time(Preliminary Report)

A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.

Space-Bounded Reducibility among Combinatorial Problems

  • N. Jones
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1975

Complexity Classes with Complete Problems Between P and NP-C

It is observed that language classes located between P and NP have complete problems, and characterizations of these classes are found using robust machines with bounded access to the oracle, and in terms of nondeterministic complexity classes with polylog running time.

Lower bounds for natural proof systems

  • D. Kozen
  • Computer Science
    18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
  • 1977
A lower space bound of n/log(n) is shown for the proof system for the PTIME complete theory and a lower length bound of 2cn/log('n'): length of polynomial space for the PSPACE complete theory.

An Introduction to Automata Theory

Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial

Introduction to Automata Theory, Languages and Computation

The Boolean formula value problem is in ALOGTIME

This paper shows that both the Boolean formula value problem and the more general problem of recognizing a parenthesis context-free grammar have alternating log time algorithms and gives a precise characterisation of the computational complexity of determining the truth value of a Boolean formula.

A Taxonomy of Problems with Fast Parallel Algorithms

  • S. Cook
  • Computer Science, Mathematics
    Inf. Control.
  • 1985

Refining Nondeterminism in Relativized Polynomial-Time Bounded Computations

The classes of languages acceptable by polynomial-time bounded Turing machines making at most $g(n)$ nondeterministic moves on inputs of length n are studied and relativized classes are studied.