542 research outputs found
Weighted Branching Simulation Distance for Parametric Weighted Kripke Structures
This paper concerns branching simulation for weighted Kripke structures with
parametric weights. Concretely, we consider a weighted extension of branching
simulation where a single transitions can be matched by a sequence of
transitions while preserving the branching behavior. We relax this notion to
allow for a small degree of deviation in the matching of weights, inducing a
directed distance on states. The distance between two states can be used
directly to relate properties of the states within a sub-fragment of weighted
CTL. The problem of relating systems thus changes to minimizing the distance
which, in the general parametric case, corresponds to finding suitable
parameter valuations such that one system can approximately simulate another.
Although the distance considers a potentially infinite set of transition
sequences we demonstrate that there exists an upper bound on the length of
relevant sequences, thereby establishing the computability of the distance.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
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
A Quantitative Characterization of Weighted Kripke Structures in Temporal Logic
We extend the usual notion of Kripke structures with a weighted transition relation and generalize the classical Boolean interpretation of CTL to a map which assigns to states and temporal formulae a real-valued distance describing the degree of satisfaction. We describe a general approach to obtaining quantitative interpretations for a generic extension of the CTL syntax and show that, for one such interpretation, the logic is both adequate and expressive with respect to quantitative bisimulation
Temporal specifications with accumulative values
Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable
IST Austria Technical Report
There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable
Distances for Weighted Transition Systems: Games and Properties
We develop a general framework for reasoning about distances between
transition systems with quantitative information. Taking as starting point an
arbitrary distance on system traces, we show how this leads to natural
definitions of a linear and a branching distance on states of such a transition
system. We show that our framework generalizes and unifies a large variety of
previously considered system distances, and we develop some general properties
of our distances. We also show that if the trace distance admits a recursive
characterization, then the corresponding branching distance can be obtained as
a least fixed point to a similar recursive characterization. The central tool
in our work is a theory of infinite path-building games with quantitative
objectives.Comment: In Proceedings QAPL 2011, arXiv:1107.074
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