## 595 Citations

### The Complementation Problem for Büchi Automata with Applications to Temporal Logic (Extended Abstract)

- Mathematics, Computer ScienceICALP
- 1985

This work uses a construction that involves only an exponential blow-up in the size of the automaton to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove the complexity hierarchy result for quantified propositionalporal logic.

### An Automata Theoretic Decision Procedure for the Propositional Mu-Calculus

- MathematicsInf. Comput.
- 1989

### Alternating Automata: Checking Truth and Validity for Temporal Logics

- Computer Science
- 1998

The simple combinatorial structures that emerge from the automata-theoretic approach decouple the logical and algorithmic components of truth and validity checking and yield clean and essentially optimal algorithms for both problems.

### Automata-Theoretic Decision Procedures for Information Logics

- Computer ScienceFundam. Informaticae
- 2002

An EXPTIME decision procedure based on the emptiness problem of Buchi automata on infinite trees for the very expressive information logic SIM designed for reasoning about information systems is defined.

### Alternating Automata and Program Verification

- Computer ScienceComputer Science Today
- 1995

The simple combinatorial structures that emerge from the automata-theoretic approach decouple the logical and algorithmic components of finite-state-program verification and yield clear and general verification algorithms.

### Alternating Automata: Unifying Truth and Validity Checking for Temporal Logics

- Computer ScienceCADE
- 1997

The simple combinatorial structures that emerge from the automata-theoretic approach decouple the logical and algorithmic components of truth and validity checking and yield clean and essentially optimal algorithms for both problems.

### Reasoning About Infinite Computations

- Computer ScienceInf. Comput.
- 1994

This work investigates extensions of temporal logic by connectives defined by finite automata on infinite words and shows that they do not increase the expressive power of the logic or the complexity of the decision problem.

### PSPACE Automata for Description Logics

- Computer ScienceDescription Logics
- 2006

The usefulness of segmentable automata is demonstrated by reproving the known PSpace result for satisfiability of ALC concepts with respect to acyclic.

### The Complementation Problem for Büchi Automata with Appplications to Temporal Logic

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1987

### The complexity of tree automata and logics of programs

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

It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete, and it follows that satisfiability for propositional dynamic logic with a repetition construct and for the propositional mu-calculus can be tests in deterministic single exponential time.

## References

SHOWING 1-10 OF 45 REFERENCES

### Automata theoretic techniques for modal logics of programs: (Extended abstract)

- Computer ScienceSTOC '84
- 1984

A new technique for obtaining decision procedures for modal logics of programs using a new class of finite automata on infinite trees for which the emptiness problem can be solved in polynomial time.

### Propositional Dynamic Logic of Regular Programs

- Computer Science, PhilosophyJ. Comput. Syst. Sci.
- 1979

### The Emptiness Problem for Automata on Infinite Trees

- Computer Science, MathematicsSWAT
- 1972

The proof reduces the emptiness problem for automata on infinite trees to that for Automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitely-generable tree.

### Deterministic Propositional Dynamic Logic: Finite Models, Complexity, and Completeness

- PhilosophyJ. Comput. Syst. Sci.
- 1982

### Models of program logics

- Computer Science20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979

The common theory has already been shown to be complete in deterministic exponential time; the simpler proof of the upper bound is given.

### Propositional Dynamic Logic of Looping and Converse Is Elementarily Decidable

- Computer ScienceInf. Control.
- 1982

### Improved upper and lower bounds for modal logics of programs

- Computer ScienceSTOC '85
- 1985

It is shown that the satisfiability problems for Streett's delta-<italic>PDL</italic>.

### The temporal logic of branching time

- PhilosophyPOPL '81
- 1981

The following metatheoretical results are proven: 1) an exponential decision procedure for satisfiability; 2) a finite model property; 3) the completeness of an axiomatization.