## 557 Citations

### Minimal Separating Sets for Acceptance Conditions in Muller Automata

- Computer ScienceTheor. Comput. Sci.
- 2000

### Control Theory, Modal Logic and Games

- Computer ScienceHybrid Systems
- 1996

It is shown that if the regulator can in some way guarantee satisfaction of a specification, then it can do so acting as a deterministic finite automaton, and it is determined that there is none.

### Avoiding Determinization

- Computer Science21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
- 2006

This work shows how the use of universal automata simplifies significantly known complementation constructions for automata on infinite words, known decision procedures for branching temporal logics, known synthesis algorithms, and other applications that are now based on determinization.

### The Role of Büchi’s Automata in Computing Science

- Computer Science
- 1990

By the end of the 1960s, Rabin had shown how automata on infinite trees could be used to show decidability of a surprisingly rich class of logical theories including the basic monadic second-order theory of multiple successors (SnS).

### Control of omega-Automata, Church's Problem, and the Emptiness Problem for Tree omega-Automata

- Computer ScienceCSL
- 1991

Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automaton on infinite strings based on a fixpoint representation of the controllability subset.

### Decision problems forω-automata

- Computer Science, MathematicsMathematical systems theory
- 2005

This paper considers various definitions for machines of this type, including ones introduced by Biichi and McNaughton, and classify the complexity of definable sets of sequences for each type of finite automaton.

### On the complexity of omega -automata

- Computer Science[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
- 1988

The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.

### Ensembles reconnaissables de mots biinfinis

- Mathematics, Computer ScienceSTOC '82
- 1982

The aim of this paper is to build an analogous theorem for two-sided infinite sequences of the theorem of B-&-uuml;chi and Mc Naughton: the recognizable sets of biinfinite words are the finite boolean combinations of deterministic ones (Theorem 3.1).

### SOLVING SEQUENTIAL CONDITIONS BY FINITE-STATE STRATEGIESO

- Mathematics
- 2010

Our main purpose is to present an algorithm which decides whether or not a condition &(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This…

## References

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### Infinite sequences and finite machines

- MathematicsSWCT
- 1963

A regular set is a set of possible state sequences of an inputless, nondeterministic machine that may either terminate in some equilibrium condition, or else the machine may pass from one state to another without ever reaching equ~librium.

### Representation of Events in Nerve Nets and Finite Automata

- Computer Science
- 1951

This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.

### Fundamental Concepts in the Theory of Systems," Tech. Report No. 57-624 (Wright Air Development Center, Cincinnati)

- 1957