Kripke structure

This article describes Kripke structures as used in model checking.

State updates are a means of describing state transitions in a Kripke structure.

Temporal logics are traditionally interpreted in terms of Kripke structures.

This syntactic characterization is given semantic content through so-called Kripke structures.

Modal logic is most commonly interpreted in terms of possible world semantics or Kripke structures.

These sequences can be viewed as a word on a path of a Kripke structure (an ω-word over alphabet 2).

Note however that there is a difference in the interpretation between Kripke structures and Büchi automata.

If a state of the Kripke structure satisfies a state formula it is denoted .

Since R is left-total, it is always possible to construct an infinite path through the Kripke structure.

The underlying mathematical model of the logic-based approach are Kripke structures, while the event-based approach employs the related Aumann structures.

A Kripke structure is a variation of nondeterministic automaton proposed by Saul Kripke, used in model checking to represent the behavior of a system.

In model checking, a state transition system is sometimes defined to include an additional labeling function for the states as well, resulting in a notion that encompasses that of Kripke structure.

With this definition, a Kripke structure may be identified with a Moore machine with a singleton input alphabet, and with the output function being its labeling function.

As we mentioned above, the logic-based approach is built upon the possible worlds model, the semantics of which are often given definite form in Kripke structures, also known as Kripke models.

Clarke et al. redefine a Kripke structure as a set of transitions (instead of just one), which is equivalent to the labeled transitions above, when they define the semantics of modal μ-calculus.