Towards a Notion of Unsatisfiable Cores for LTL

Abstract

Abstract. Unsatisfiable cores, i.e., parts of an unsatisfiable formula that are themselves unsatisfiable, have important uses in debugging specifications, speeding up search in model checking or SMT, and generating certificates of unsatisfiability. While unsatisfiable cores have been well investigated for Boolean SAT and constraint programming, the notion of unsatisfiable cores for temporal logics such as LTL has not received much attention. In this paper we investigate notions of unsatisfiable cores for LTL that arise from the syntax tree of an LTL formula, from converting it into a conjunctive normal form, and from proofs of its unsatisfiability. The resulting notions are more fine-granular than existing ones.

An iterative approach to synthesize business process templates from compliance rules

“…Hantry and Hacid proposed a conflict-driven tableau depth-first-search for LTL, the complexity of their approach is theoretically EXPTIME [25]. Schuppan demonstrated approaches to compute unsatisfiable cores of LTL formulae from various aspects [24], but there was no requirement to find a minimal one.…”

“…Various approaches attempt to find the explanations for the inconsistency of a set G of given formulae [23][24][25][26].…”

Analyzing Unsynthesizable Specifications for High-Level Robot Behavior Using LTLMoP

“…The most recent version of LTLMoP can be downloaded online 1 . There has been considerable previous work on analyzing unsatisfiable and unrealizable LTL formulas [2,[4][5][6]14]. Our work is most closely related to that of [9], who present an interactive tool, RATSY [3] for demonstrating specification unrealizability.…”

Aalta: an LTL satisfiability checker over Infinite/Finite traces

“…The pltl 1 solver is a representative of this approach. The temporal-resolution approach explores the unsatisfiable core using a deductive system [10]. The tool TRP++ [10] is a representative of this approach.…”

“…The temporal-resolution approach explores the unsatisfiable core using a deductive system [10]. The tool TRP++ [10] is a representative of this approach. Our own approach [5,7] follows the automata-theoretic approach [12] and reduces satisfiability checking to automaton emptiness checking, which we perform by using two heuristics: on-the-fly search and obligation sets.…”