310 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
redundancy coverag
Interestingness of traces in declarative process mining: The janus LTLPf Approach
Declarative process mining is the set of techniques aimed at extracting behavioural constraints from event logs. These constraints are inherently of a reactive nature, in that their activation restricts the occurrence of other activities. In this way, they are prone to the principle of ex falso quod libet: they can be satisfied even when not activated. As a consequence, constraints can be mined that are hardly interesting to users or even potentially misleading. In this paper, we build on the observation that users typically read and write temporal constraints as if-statements with an explicit indication of the activation condition. Our approach is called Janus, because it permits the specification and verification of reactive constraints that, upon activation, look forward into the future and backwards into the past of a trace. Reactive constraints are expressed using Linear-time Temporal Logic with Past on Finite Traces (LTLp f). To mine them out of event logs, we devise a time bi-directional valuation technique based on triplets of automata operating in an on-line fashion. Our solution proves efficient, being at most quadratic w.r.t. trace length, and effective in recognising interestingness of discovered constraints
Coverage and Vacuity in Network Formation Games
The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter
Bounded Satisfiability for PCTL
While model checking PCTL for Markov chains is decidable in polynomial-time,
the decidability of PCTL satisfiability, as well as its finite model property,
are long standing open problems. While general satisfiability is an intriguing
challenge from a purely theoretical point of view, we argue that general
solutions would not be of interest to practitioners: such solutions could be
too big to be implementable or even infinite. Inspired by bounded synthesis
techniques, we turn to the more applied problem of seeking models of a bounded
size: we restrict our search to implementable -- and therefore reasonably
simple -- models. We propose a procedure to decide whether or not a given PCTL
formula has an implementable model by reducing it to an SMT problem. We have
implemented our techniques and found that they can be applied to the practical
problem of sanity checking -- a procedure that allows a system designer to
check whether their formula has an unexpectedly small model
Quantified Linear Temporal Logic over Probabilistic Systems with an Application to Vacuity Checking
Quantified linear temporal logic (QLTL) is an ?-regular extension of LTL allowing quantification over propositional variables. We study the model checking problem of QLTL-formulas over Markov chains and Markov decision processes (MDPs) with respect to the number of quantifier alternations of formulas in prenex normal form. For formulas with k{-}1 quantifier alternations, we prove that all qualitative and quantitative model checking problems are k-EXPSPACE-complete over Markov chains and k{+}1-EXPTIME-complete over MDPs.
As an application of these results, we generalize vacuity checking for LTL specifications from the non-probabilistic to the probabilistic setting. We show how to check whether an LTL-formula is affected by a subformula, and also study inherent vacuity for probabilistic systems
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