Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete

@inproceedings{Schewe2010BeyondHD,
  title={Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete},
  author={Sven Schewe},
  booktitle={Foundations of Software Technology and Theoretical Computer Science},
  year={2010}
}
  • S. Schewe
  • Published in
    Foundations of Software…
    2010
  • Computer Science
In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic \buchi, \cobuchi, and parity automata play a similar role in the recognition of $\omega$-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic \buchi\ and parity automata has remained… 

Figures from this paper

Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata

It is argued that minimisation of finite automata, hyper-minimisation, relaxed minimisation, and the minimised of deterministic Buchi (or Co-Buchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right.

Minimising Good-for-Games automata is NP complete

It is shown for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Buchi, Co-Buchi, and parity G FG automata, a surprisingly straight forward generalisation of the proofs from deterministic Buchi automata.

Canonicity in GFG and Transition-Based Automata

Limiting attention to the safe components is useful, and implies that the only minimal tDCWs that have no canonical form are these for which the transition to the GFG model results in strictly smaller automaton, which do have a canonical minimal form.

Minimization and Canonization of GFG Transition-Based Automata

Their minimization algorithm is based on a sequence of transformations the authors apply to the automaton, on top of which a minimal quotient automaton is defined, and all minimal automata have isomorphic safe components and once they saturate the automata with $\alpha$-transitions, they get full isomorphism.

Learning Deterministic Automata on Infinite Words

This framework is similar to the one of Angluin’s L∗-algorithm, but the crucial difference is that the queries about the loop index depend on a particular automaton representing an ω-regular language, which allows it to bypass the NP-hardness coming from the minimisation problem for deterministic Büchi automata and provide a polynomial-time algorithm.

Constructing deterministic $\omega$-automata from examples by an extension of the RPNI algorithm

It is proved that active learning with membership and equivalence queries is not easier for automata with an informative right congruence than for general deterministic ω-automata in the limit with polynomial time and data.

Constructing deterministic ω-automata from examples by an extension of the RPNI algorithm

It is proved that active learning with membership and equivalence queries is not easier for automata with an informative right congruence than for general deterministic ω-automata in the limit with polynomial time and data.

Optimal Hyper-Minimization

This paper presents a new algorithm for hyper-minimizing minimized deterministic finite state automata that is further improved to return a DFA that commits the least number of errors at the expense of an increased (quadratic) run-time.

Minimization of Limit-Average Automata

This paper presents a minimization algorithm for LimAvgautomata, and presents an extension of Angluin’s L∗-algorithm with syntactic queries, which learns in polynomial time a LimAvg-automaton equivalent to the target one.

Minimization and Learning of Deterministic $\omega$-Automata in the Presence of Don't Care Words

It is proved that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don’t care words and that an active learning algorithm for WDBA is extended to the setting with an additional set ofDon’s care words with trivial right-congruence.

References

SHOWING 1-10 OF 30 REFERENCES

Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata

It is argued that minimisation of finite automata, hyper-minimisation, relaxed minimisation, and the minimised of deterministic Buchi (or Co-Buchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right.

Tighter Bounds for the Determinisation of Büchi Automata

This paper proposes a determinisation technique that is simpler than the constructions of Safra, Piterman, and Muller and Schupp, because it separates the principle acceptance mechanism from the concrete acceptance condition.

Hyper-minimisation Made Efficient

The previously known $\mathcal O (|\Sigma|n^2)$ solution is improved by giving an expected time algorithm for this problem, where |?| is the size of the (potentially partial) transition function.

Hyper-minimizing minimized deterministic finite state automata

We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a hyper-minimized DFA, which may have fewer states than the classically minimized

HYPER-MINIMIZATION IN O(n2)

  • A. Badr
  • Computer Science
    Int. J. Found. Comput. Sci.
  • 2008
A technique is suggested that combines this hyper-minimization with the well-studied notion of a deterministic finite cover automaton, or DFCA, thereby extending the applicability of DFCAs from finite to infinite regular languages.

From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata

  • N. Piterman
  • Computer Science
    21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
  • 2006
This paper shows how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions and revisits Safra's determinization constructions.

Minimising Deterministic Büchi Automata Precisely Using SAT Solving

We show how deterministic Buchi automata can be fully minimised by reduction to the satisfiability (SAT) problem, yielding the first automated method for this task. Size reduction of such ω-automata

Distributed reactive systems are hard to synthesize

  • A. PnueliRoni Rosner
  • Computer Science
    Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
  • 1990
It is shown that the problem of realizing a given propositional specification over a given architecture is undecidable, and it is nonelementarily decidable for the very restricted class of hierarchical architectures.

Computing the Rabin Index of a Parity Automaton

The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n(2)c) where c is the cardinality of the alphabet. The number of values used