Reasoning About Infinite Computations

@article{Vardi1994ReasoningAI,
  title={Reasoning About Infinite Computations},
  author={Moshe Y. Vardi and Pierre Wolper},
  journal={Inf. Comput.},
  year={1994},
  volume={115},
  pages={1-37}
}
We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping, and repeating) for the automata. It turns out, however that these logics all have the same expressive power and that their decision problems are all PSPACE-complete. We also investigate connectives defined by alternating automata and show that they do not increase the… 

Alternating Automata: Checking Truth and Validity for Temporal Logics

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.

Alternating Automata: Unifying Truth and Validity Checking for Temporal Logics

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 Theory and Model Checking

The different classes of automata are compared in terms of expressive power and succinctness, and decision problems for them are described, and the automata-theoretic approach to system specification and verification is described.

Automata: from logics to algorithms

Translations from five different logics are reviewed, in a unified framework, into appropriate models of finite-state automata on infinite words or infinite trees, and optimal complexity bounds for satisfiability, conformance, and realizability are obtained for all logics.

Alternating Automata and Program Verification

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.

Specification and Verification using Temporal Logics

This chapter illustrates two aspects of automata theory related to linear-time temporal logic LTL used for the verification of computer systems. First, we present a translation from LTL formulae to

An automata-theoretic approach to constraint LTL

Constructing Automata from Temporal Logic Formulas: A Tutorial

  • P. Wolper
  • Computer Science
    European Educational Forum: School on Formal Methods and Performance Analysis
  • 2000
This paper presents a tutorial introduction to the construction of finite-automata on infinite words from linear-time temporal logic formulas, and describes a first construction whose correctness is quite direct to establish, but whose behavior is always equal to the worst-case upper bound.

Integrate Action Formalisms into Linear Temporal Description Logics

This paper abstracts from the actual execution sequences of a non-terminating program by considering infinite sequences of actions defined by a Büchi automaton, and assumes that the logic underlying the action formalism is a decidable description logic rather than full first-order predicate logic.

Alternating automata and temporal logic normal forms

...

References

SHOWING 1-10 OF 54 REFERENCES

Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time

The authors give a very simple uniform explanation of the persistence of exponential decidability and characterize the weak monadic theory of the tree; it turns out that weak alternating automata greatly simplify design procedures.

Propositional Dynamic Logic of Regular Programs

Finite Automata and Their Decision Problems

Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.

Propositional Dynamic Logic of Flowcharts

Automatic verification of probabilistic concurrent finite state programs

  • Moshe Y. Vardi
  • Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
An automata-theoretic approach is described, whereby probabilistic quantification over sets of computations is reduced to standard quantificationover individual computations, and a new determinization construction for ω-automata is used to improve the time complexity of the algorithm by two exponentials.
...