A Logical Study of Distributed Transition Systems

@article{Lodaya1995ALS,
  title={A Logical Study of Distributed Transition Systems},
  author={Kamal Lodaya and Rohit Parikh and Ramaswamy Ramanujam and P. S. Thiagarajan},
  journal={Inf. Comput.},
  year={1995},
  volume={119},
  pages={91-118}
}
We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an addition-based temporal logic in which one can explicity talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment… 

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References

SHOWING 1-10 OF 51 REFERENCES
A logic for distributed transition systems
TLDR
This work presents a logical characterization of a particular aspect of concurrency called the concurrent step notion, and implies that satisfiability in the logical system is decidable.
Concurrent Transition Systems
  • E. W. Stark
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1989
Models for Concurrency
This is a draft version of a chapter for the Handbook of Logic and the Foundations of Computer Science, Oxford University Press. The final draft can be found as DAIMI PB 463. It surveys a range of
Event Structures
  • G. Winskel
  • Computer Science
    Advances in Petri Nets
  • 1986
TLDR
The mathematical theory of event structures is presented, how they are related to Petri nets and Scott domains, and how they can be used to provide semantics to programming languages for parallel processes as welt as languages with higher types are surveyed.
Basic notions of trace theory
TLDR
The theory of traces can be used as a tool for reasoning about nets and it is hoped that applying this theory one can get a calculus of the concurrent processes analogous to that available for sequential systems.
Petri Nets, Event Structures and Domains
TLDR
The general aim of the paper is to find a theory of concurrency combining the approaches of Petri and Scott, and to connect the abstract ideas of events and domains of information, by showing how causal nets induce certain kinds of domains where the information points are certain sets of events.
Algebraic laws for nondeterminism and concurrency
TLDR
The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.
Concurrency and Automata on Infinite Sequences
  • D. Park
  • Computer Science
    Theoretical Computer Science
  • 1981
TLDR
A general method for proving/deciding equivalences between omega-regular languages, whose recognizers are modified forms of Buchi or Muller-McNaughton automata, derived from Milner's notion of “simulation” is obtained.
...
...