Abstract
In the present paper, we introduce the backdoor set approach into the field of temporal logic for the global fragment of linear temporal logic. We study the parameterized complexity of the satisfiability problem parameterized by the size of the backdoor. We distinguish between backdoor detection and evaluation of backdoors into the fragments of Horn and Krom formulas. Here we classify the operator fragments of globally-operators for past/future/always, and the combination of them. Detection is shown to be fixed-parameter tractable whereas the complexity of evaluation behaves differently. We show that for Krom formulas the problem is paraNP-complete. For Horn formulas, the complexity is shown to be either fixed parameter tractable or paraNP-complete depending on the considered operator fragment.
Highlights
Temporal logic is one of the most important formalism in the area of program verification and validation of specification consistency
We will consider the global fragment of LTL for formulas in separated normal form (SNF) which has been introduced by Fisher [15]
The restriction to SNF normal form is crucial for us, because it is known that syntactical restrictions of arbitrary LTL formulas such as Horn or Krom do not lead to tractability [4]
Summary
Temporal logic is one of the most important formalism in the area of program verification and validation of specification consistency. We will consider the global fragment of LTL for formulas in separated normal form (SNF) which has been introduced by Fisher [15] This normal form is a generalization of the conjunctive normal form from propositional logic to linear temporal logic with future and past modalities interpreted over the flow of time, i.e., the frame of the integers (Z,
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