395 research outputs found
On the Complexity of Computing Minimal Unsatisfiable LTL formulas
We show that (1) the Minimal False QCNF search-problem (MF-search) and the
Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE
complete because of the very expressive power of QBF/LTL, (2) we extend the
PSPACE-hardness of the MF decision problem to the MU decision problem. As a
consequence, we deduce a positive answer to the open question of PSPACE
hardness of the inherent Vacuity Checking problem. We even show that the
Inherent Non Vacuous formula search problem is also FPSPACE-complete.Comment: Minimal unsatisfiable cores For LTL causes inherent vacuity checking
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SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
Recursive Online Enumeration of All Minimal Unsatisfiable Subsets
In various areas of computer science, we deal with a set of constraints to be
satisfied. If the constraints cannot be satisfied simultaneously, it is
desirable to identify the core problems among them. Such cores are called
minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more
information about the conflicts among the constraints is obtained. However, a
full enumeration of all MUSes is in general intractable due to the large number
(even exponential) of possible conflicts. Moreover, to identify MUSes
algorithms must test sets of constraints for their simultaneous satisfiabilty.
The type of the test depends on the application domains. The complexity of
tests can be extremely high especially for domains like temporal logics, model
checking, or SMT. In this paper, we propose a recursive algorithm that
identifies MUSes in an online manner (i.e., one by one) and can be terminated
at any time. The key feature of our algorithm is that it minimizes the number
of satisfiability tests and thus speeds up the computation. The algorithm is
applicable to an arbitrary constraint domain and its effectiveness demonstrates
itself especially in domains with expensive satisfiability checks. We benchmark
our algorithm against state of the art algorithm on Boolean and SMT constraint
domains and demonstrate that our algorithm really requires less satisfiability
tests and consequently finds more MUSes in given time limits
Goal-conflict detection based on temporal satisfiability checking
Goal-oriented requirements engineering approaches propose capturing how a system should behave through the speci ca- tion of high-level goals, from which requirements can then be systematically derived. Goals may however admit subtle situations that make them diverge, i.e., not be satis able as a whole under speci c circumstances feasible within the domain, called boundary conditions . While previous work al- lows one to identify boundary conditions for con icting goals written in LTL, it does so through a pattern-based approach, that supports a limited set of patterns, and only produces pre-determined formulations of boundary conditions. We present a novel automated approach to compute bound- ary conditions for general classes of con icting goals expressed in LTL, using a tableaux-based LTL satis ability procedure. A tableau for an LTL formula is a nite representation of all its satisfying models, which we process to produce boundary conditions that violate the formula, indicating divergence situations. We show that our technique can automatically produce boundary conditions that are more general than those obtainable through existing previous pattern-based approaches, and can also generate boundary conditions for goals that are not captured by these patterns
Low-Effort Specification Debugging and Analysis
Reactive synthesis deals with the automated construction of implementations
of reactive systems from their specifications. To make the approach feasible in
practice, systems engineers need effective and efficient means of debugging
these specifications.
In this paper, we provide techniques for report-based specification
debugging, wherein salient properties of a specification are analyzed, and the
result presented to the user in the form of a report. This provides a
low-effort way to debug specifications, complementing high-effort techniques
including the simulation of synthesized implementations.
We demonstrate the usefulness of our report-based specification debugging
toolkit by providing examples in the context of generalized reactivity(1)
synthesis.Comment: In Proceedings SYNT 2014, arXiv:1407.493
Linear Encodings of Bounded LTL Model Checking
We consider the problem of bounded model checking (BMC) for linear temporal
logic (LTL). We present several efficient encodings that have size linear in
the bound. Furthermore, we show how the encodings can be extended to LTL with
past operators (PLTL). The generalised encoding is still of linear size, but
cannot detect minimal length counterexamples. By using the virtual unrolling
technique minimal length counterexamples can be captured, however, the size of
the encoding is quadratic in the specification. We also extend virtual
unrolling to Buchi automata, enabling them to accept minimal length
counterexamples.
Our BMC encodings can be made incremental in order to benefit from
incremental SAT technology. With fairly small modifications the incremental
encoding can be further enhanced with a termination check, allowing us to prove
properties with BMC. Experiments clearly show that our new encodings improve
performance of BMC considerably, particularly in the case of the incremental
encoding, and that they are very competitive for finding bugs. An analysis of
the liveness-to-safety transformation reveals many similarities to the BMC
encodings in this paper. Using the liveness-to-safety translation with
BDD-based invariant checking results in an efficient method to find shortest
counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005
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