18 research outputs found
Discounting in LTL
In recent years, there is growing need and interest in formalizing and
reasoning about the quality of software and hardware systems. As opposed to
traditional verification, where one handles the question of whether a system
satisfies, or not, a given specification, reasoning about quality addresses the
question of \emph{how well} the system satisfies the specification. One
direction in this effort is to refine the "eventually" operators of temporal
logic to {\em discounting operators}: the satisfaction value of a specification
is a value in , where the longer it takes to fulfill eventuality
requirements, the smaller the satisfaction value is.
In this paper we introduce an augmentation by discounting of Linear Temporal
Logic (LTL), and study it, as well as its combination with propositional
quality operators. We show that one can augment LTL with an arbitrary set of
discounting functions, while preserving the decidability of the model-checking
problem. Further augmenting the logic with unary propositional quality
operators preserves decidability, whereas adding an average-operator makes some
problems undecidable. We also discuss the complexity of the problem, as well as
various extensions
Weighted Modal Transition Systems
Specification theories as a tool in model-driven development processes of
component-based software systems have recently attracted a considerable
attention. Current specification theories are however qualitative in nature,
and therefore fragile in the sense that the inevitable approximation of systems
by models, combined with the fundamental unpredictability of hardware
platforms, makes it difficult to transfer conclusions about the behavior, based
on models, to the actual system. Hence this approach is arguably unsuited for
modern software systems. We propose here the first specification theory which
allows to capture quantitative aspects during the refinement and implementation
process, thus leveraging the problems of the qualitative setting.
Our proposed quantitative specification framework uses weighted modal
transition systems as a formal model of specifications. These are labeled
transition systems with the additional feature that they can model optional
behavior which may or may not be implemented by the system. Satisfaction and
refinement is lifted from the well-known qualitative to our quantitative
setting, by introducing a notion of distances between weighted modal transition
systems. We show that quantitative versions of parallel composition as well as
quotient (the dual to parallel composition) inherit the properties from the
Boolean setting.Comment: Submitted to Formal Methods in System Desig
Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in FLâ‚€
Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FLâ‚€ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.Accepted to LATA 201
Weighted automata and multi-valued logics over arbitrary bounded lattices
AbstractWe show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words. We also prove that aperiodicity, star-freeness, and L-valued first-order and LTL-definability coincide. This extends classical results of Kleene, Büchi–Elgot–Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices
Definable transductions and weighted logics for texts
AbstractA text is a word together with an additional linear order on it. We study quantitative models for texts, i.e. text series which assign to texts elements of a semiring. We introduce an algebraic notion of recognizability following Reutenauer and Bozapalidis as well as weighted automata for texts combining an automaton model of Lodaya and Weil with a model of Ésik and Németh. After that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by Droste and Gastin. In order to do so, we study certain definable transductions and show that they are compatible with weighted logics
Multi-weighted Automata Models and Quantitative Logics
Recently, multi-priced timed automata have received much attention for real-time systems. These automata extend priced timed automata by featuring several price parameters. This permits to compute objectives like the optimal ratio between rewards and costs. Arising from the model of timed automata, the multi-weighted setting has also attracted much notice for classical nondeterministic automata.
The present thesis develops multi-weighted MSO-logics on finite, infinite and timed words which are expressively equivalent to multi-weighted automata, and studies decision problems for them. In addition, a Nivat-like theorem for weighted timed automata is proved; this theorem establishes a connection between quantitative and qualitative behaviors of timed automata. Moreover, a logical characterization of timed pushdown automata is given