# 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} }

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…

## 41 Citations

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

- BusinessArXiv
- 2010

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.

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### Learning Deterministic Automata on Infinite Words

- Computer ScienceECAI
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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

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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.

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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

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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

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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

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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.

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