Abstract
We consider the model checking problem for Gap-order Constraint Systems (GCS) w.r.t. the branching-time temporal logic CTL, and in particular its fragments EG and EF. GCS are nondeterministic infinitely branching processes described by evolutions of integer-valued variables, subject to Presburger c onstraints of the form x − y ≥ k, where x and y are variables or constants and k ∈ ℕ is a non-negative constant. We show that EG model checking is undecidable for GCS, while EF is decidable. In particular, this implies the decidability of strong and weak bisimulation equivalence between GCS and finite-state systems.
Highlights
Counter machines [Min67] extend a finite control-structure with unbounded memory in the form of counters that can hold arbitrarily large integers, and resemble basic programming languages
We study the decidability of model checking problems for Gap-order Constraint Systems (GCS) with fragments of computation-tree logic (CTL), namely EF and EG
While general CTL model checking of GCS is undecidable, we show that it is decidable for the logic EF
Summary
Counter machines [Min67] extend a finite control-structure with unbounded memory in the form of counters that can hold arbitrarily large integers (or natural numbers), and resemble basic programming languages. E.g., Petri nets model weaker counters that cannot be tested for zero, and have a decidable reachability problem [May84]. Gap-order constraint systems [Boz12,BP12] are another model that approximates the behavior of counter machines. They are nondeterministic infinitely branching processes described by evolutions of integer-valued variables, subject to Presburger constraints of the form x − y ≥ k, where x and y are variables or constants and k ∈ N is a non-negative constant. Model checking GCS is decidable for the logic ECT L∗, but undecidable for ACT L∗, which are the existential and universal fragments of CT L∗ respectively. We study the decidability of model checking problems for GCS with fragments of computation-tree logic (CTL), namely EF and EG. An immediate consequence of our decidability result for EF is that strong and weak bisimulation equivalence are decidable between GCS and finite-state systems
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