LTL Satisfiability Checking Revisited

Abstract

Abstract-We propose a novel algorithm for the satisfiability problem for Linear Temporal Logic (LTL). Existing approaches first transform the LTL formula into a Büchi automaton and then perform an emptiness checking of the resulting automaton. Instead, our approach works on-the-fly by inspecting the formula directly, thus enabling finding a satisfying model quickly without constructing the full automaton. This makes our algorithm particularly fast for satisfiable formulas. We report on a prototype implementation, showing that our approach significantly outperforms state-of-the-art tools.

Specification: The Biggest Bottleneck in Formal Methods and Autonomy

“…In [45] we designed a portfolio approach consisting of 30 new encodings for LTL satisfiability via symbolic model checking that performed up to exponentially faster than was previously possible. In [33,34], the explicit approach was improved, circumventing explicit-state model checking and solving the LTL satisfiability problem directly using techniques borrowed from propositional SAT solving. Today, the (freely available) tools PANDA [45] and Aalta [34], represent the state of the art in symbolic (via the nuXmv model checker) and explicit LTL satisfiability checking, respectively.…”

Efficient Scalable Verification of LTL Specifications

“…Such automata are used by SPOT [26], which is claimed to be the best explicit LTL-to-Büchi automata translator for satisfiability checking purposes based on the experiments carried out in [23]. Li et al [27] present a novel on-the-fly construction of Büchi automata from LTL formulae that is particularly well suited for finding models of LTL formulae when they exist. Given the different nature of our approach with respect to automata-based ones, however, we did not compare our approach against them, and focused on similar, BSC-based approaches instead.…”

Aalta: an LTL satisfiability checker over Infinite/Finite traces

“…Aalta implements the obligation-based LTL satisfiability checking algorithms that are proposed in our previous work [5,6,7]. We first introduce briefly the obligation formula, which is the key concept of our approach and then present the main decision procedure behind Aalta.…”

“…The framework of Aalta is based on LTL transition systems, which we proposed in previous work [5]. To the best of our knowledge, this is the first tool to directly support LTL satisfiability checking over both infinite and finite traces.…”

“…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.…”