# 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.

### Mechanizing the Minimization of Deterministic Generalized Büchi Automata

• Computer Science
FORTE
• 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.

### SAT-based Minimization of Deterministic ω-Automata

• Computer Science
• 2015
This tool, that relies on a SAT-based encoding of the problem, can be used to provide minimal ω-automata equivalent to given properties, for different acceptance conditions.

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

• Computer Science
TACAS
• 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

### ACTL ∩ LTL Synthesis

A synthesis approach is described that inherits the efficiency of generalized reactivity(1) synthesis, but is significantly richer in terms of expressivity.

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

• Computer Science
LPAR
• 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

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.

### Generalized simulation relations with applications in automata theory

The central topic of this thesis is the design of GFQ equivalences for Buchi automata, and how simulation relations have recently been applied to significantly optimize exact (exponential) language inclusion algorithms, thus extending their practical applicability.

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

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 Science
CAV
• 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 Science
GandALF
• 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.

## 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.

### Bounded model checking

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 Science
CONCUR
• 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

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 Science
CAV
• 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

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 Science
ISAAC
• 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 Science
Int. 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 Science
ICALP
• 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.