# Minimising Deterministic Büchi Automata Precisely Using SAT Solving

@inproceedings{Ehlers2010MinimisingDB, title={Minimising Deterministic B{\"u}chi Automata Precisely Using SAT Solving}, author={R{\"u}diger Ehlers}, booktitle={SAT}, year={2010} }

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 is an important step in probabilistic model checking as well as synthesis of finite-state systems. Our experiments demonstrate that state-of-the-art SAT solvers are capable of solving the resulting satisfiability problem instances quickly, making the approach presented valuable in practice.

## 24 Citations

### Mechanizing the Minimization of Deterministic Generalized Büchi Automata

- Computer ScienceFORTE
- 2014

This work surveys techniques used to obtain and minimize DBAs for different classes of properties and presents benchmarks using a framework that implements all these techniques.

### Minimization of Visibly Pushdown Automata Using Partial Max-SAT

- Computer ScienceTACAS
- 2017

We consider the problem of state-space reduction for nondeterministic weakly-hierarchical visibly pushdown automata (Vpa). Vpa recognize a robust and algorithmically tractable fragment of…

### SAT-Based Minimization of Deterministic \omega -Automata

- Computer ScienceLPAR
- 2015

This tool, that relies on a SAT-based encoding of the problem, can be used to provide minimal $\omega $$-automata equivalent to given properties, for different acceptance conditions.

### 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.

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

- Computer ScienceFSTTCS
- 2010

The NP-completeness of the problem of minimising deterministic automata over finite and infinite words is established, and the introduction of almost equivalence is introduced, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalenced automata.

### Acacia+, a Tool for LTL Synthesis

- Computer ScienceCAV
- 2012

We present Acacia+, a tool for solving the LTL realizability and synthesis problems. We use recent approaches that reduce these problems to safety games, and can be solved efficiently by symbolic…

### Learn with SAT to Minimize Büchi Automata

- Computer ScienceGandALF
- 2012

The minimization procedure for nondeterministic Buchi automata (NBA) is described, which can be seen as an instance of a generic learning algorithm based on a "minimally adequate teacher" in the sense of Angluin.

### Rule-Based Form for Stream Constraints

- Computer ScienceCOORDINATION
- 2018

This work proposes stream constraints as an alternative to constraint automata that avoids state space explosions and introduces a rule-based form for stream constraints that can avoid transition space explosions.

### Deciding Monadic Second Order Logic over \omega ω -Words by Specialized Finite Automata

- Computer ScienceIFM
- 2016

An efficient algorithm for homomorphisms in this representation of regular languages by regular languages is developed, which is essential for deciding MSO, and the experimental evaluation suggests that loop automata are indeed well suited for decided MSO overω-words efficiently.

### Learning Properties in LTL ∩ ACTL from Positive Examples Only

- Computer Science2020 Formal Methods in Computer Aided Design (FMCAD)
- 2020

The proposed algorithm reduces the problem of learning a universal very-weak automaton to the enumeration of elements in the Pareto front of a specifically-designed monotonous function and uses classical automaton minimization to obtain a concise, finite-state representation of the learned property.

## References

SHOWING 1-10 OF 25 REFERENCES

### Experiments with Deterministic ω-Automata for Formulas of Linear Temporal Logic

- Computer Science
- 2005

Safra’s determinization algorithm is studied in detail, several heuristics that attempt to decrease the size of the resulting automata are presented and experimental results are reported on.

### Efficient minimization of deterministic weak omega-automata

- Computer ScienceInf. Process. Lett.
- 2001

### Bounded model checking

- Computer ScienceAdv. Comput.
- 2003

A considerable part of this chapter discusses complete extensions, including k-induction and interpolation, which allow to prove properties in Bounded Model Checking.

### Optimizing Büchi Automata

- Computer ScienceCONCUR
- 2000

A family of optimizations implemented in a translation from a linear temporal logic to Buchi automata can enhance the efficiency of model checking, as practiced in tools such as SPIN.

### 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.

### Fast LTL to Büchi Automata Translation

- Computer ScienceCAV
- 2001

An algorithm to generate Buchi automata from LTL formulae is presented and compared with Spin: the experiments show that the algorithm is much more efficient than Spin.

### Analysis of Recursive Game Graphs Using Data Flow Equations

- Computer ScienceVMCAI
- 2004

Given a finite-state abstraction of a sequential program with potentially recursive procedures and input from the environment, whether there are input sequences that can drive the system into “bad/good” executions is checked.

### Deterministic w Automata vis-a-vis Deterministic Buchi Automata

- Computer ScienceISAAC
- 1994

It is proved that a deterministic L- (DLA) or Rabin automaton (DRA), unlike deterministic Muller or Streett automata, is Buchi-type if and only if its language is realizable as a DBA, which means DBA are as compact as DRA or DLA.

### Typeness for omega-regular Automata

- Computer ScienceInt. J. Found. Comput. Sci.
- 2006

A complete picture of typeness for the weak, Buchi, co-Buchi, Rabin, and Streett acceptance conditions is given, and its usefulness is discussed.

### Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata

- Computer ScienceICALP
- 2001

It is shown that, unlike fair simulation, delayed simulation preserves the automaton language upon quotienting, and that it allows substantially better state reduction than direct simulation.