114,148 research outputs found
Model-checking Quantitative Alternating-time Temporal Logic on One-counter Game Models
We consider quantitative extensions of the alternating-time temporal logics
ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in
which the value of a counter can be compared to constants using equality,
inequality and modulo constraints. We interpret these logics in one-counter
game models which are infinite duration games played on finite control graphs
where each transition can increase or decrease the value of an unbounded
counter. That is, the state-space of these games are, generally, infinite. We
consider the model-checking problem of the logics QATL and QATLs on one-counter
game models with VASS semantics for which we develop algorithms and provide
matching lower bounds. Our algorithms are based on reductions of the
model-checking problems to model-checking games. This approach makes it quite
simple for us to deal with extensions of the logical languages as well as the
infinite state spaces. The framework generalizes on one hand qualitative
problems such as ATL/ATLs model-checking of finite-state systems,
model-checking of the branching-time temporal logics CTL and CTLs on
one-counter processes and the realizability problem of LTL specifications. On
the other hand the model-checking problem for QATL/QATLs generalizes
quantitative problems such as the fixed-initial credit problem for energy games
(in the case of QATL) and energy parity games (in the case of QATLs). Our
results are positive as we show that the generalizations are not too costly
with respect to complexity. As a byproduct we obtain new results on the
complexity of model-checking CTLs in one-counter processes and show that
deciding the winner in one-counter games with LTL objectives is
2ExpSpace-complete.Comment: 22 pages, 12 figure
Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)
We revisit the classic problem of proving safety over parameterised
concurrent systems, i.e., an infinite family of finite-state concurrent systems
that are represented by some finite (symbolic) means. An example of such an
infinite family is a dining philosopher protocol with any number n of processes
(n being the parameter that defines the infinite family). Regular model
checking is a well-known generic framework for modelling parameterised
concurrent systems, where an infinite set of configurations (resp. transitions)
is represented by a regular set (resp. regular transducer). Although verifying
safety properties in the regular model checking framework is undecidable in
general, many sophisticated semi-algorithms have been developed in the past
fifteen years that can successfully prove safety in many practical instances.
In this paper, we propose a simple solution to synthesise regular inductive
invariants that makes use of Angluin's classic L* algorithm (and its variants).
We provide a termination guarantee when the set of configurations reachable
from a given set of initial configurations is regular. We have tested L*
algorithm on standard (as well as new) examples in regular model checking
including the dining philosopher protocol, the dining cryptographer protocol,
and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and
German). Our experiments show that, despite the simplicity of our solution, it
can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape
Improving Saturation-based Bounded Model Checking
Formal verification is becoming a fundamental step in assuring the correctness of safety-critical systems. Since these systems are often asynchronous and even distributed, their verification requires methods that can deal with huge or even infinite state spaces. Model checking is one of the current techniques to analyse the behaviour of systems, as part of the verification process. In this paper a symbolic bounded model checking algorithm is presented that relies on efficient saturation-based methods. The previous approaches are extended with new bounded state space exploration strategies. In addition, constrained saturation is also introduced to improve the efficiency of bounded model checking. Our measurements confirm that these approaches do not only offer a solution to deal with infinite state spaces, but in many cases they even outperform the original methods
An expectation transformer approach to predicate abstraction and data independence for probabilistic programs
In this paper we revisit the well-known technique of predicate abstraction to
characterise performance attributes of system models incorporating probability.
We recast the theory using expectation transformers, and identify transformer
properties which correspond to abstractions that yield nevertheless exact bound
on the performance of infinite state probabilistic systems. In addition, we
extend the developed technique to the special case of "data independent"
programs incorporating probability. Finally, we demonstrate the subtleness of
the extended technique by using the PRISM model checking tool to analyse an
infinite state protocol, obtaining exact bounds on its performance
Abstraction and Learning for Infinite-State Compositional Verification
Despite many advances that enable the application of model checking
techniques to the verification of large systems, the state-explosion problem
remains the main challenge for scalability. Compositional verification
addresses this challenge by decomposing the verification of a large system into
the verification of its components. Recent techniques use learning-based
approaches to automate compositional verification based on the assume-guarantee
style reasoning. However, these techniques are only applicable to finite-state
systems. In this work, we propose a new framework that interleaves abstraction
and learning to perform automated compositional verification of infinite-state
systems. We also discuss the role of learning and abstraction in the related
context of interface generation for infinite-state components.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
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A Monte Carlo model checker for probabilistic LTL with numerical constraints
We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc).
We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation
using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking
of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or
stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach
allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints
over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes
one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of
variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on
intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical
systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach
for the structured formal engineering of biological systems
Predicate Abstraction with Indexed Predicates
Predicate abstraction provides a powerful tool for verifying properties of
infinite-state systems using a combination of a decision procedure for a subset
of first-order logic and symbolic methods originally developed for finite-state
model checking. We consider models containing first-order state variables,
where the system state includes mutable functions and predicates. Such a model
can describe systems containing arbitrarily large memories, buffers, and arrays
of identical processes. We describe a form of predicate abstraction that
constructs a formula over a set of universally quantified variables to describe
invariant properties of the first-order state variables. We provide a formal
justification of the soundness of our approach and describe how it has been
used to verify several hardware and software designs, including a
directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International
Conference on Verification, Model Checking and Abstract Interpretation
(VMCAI'04), LNCS 2937, pages = 267--28
Algebraic model checking for discrete linear dynamical systems
Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass of infinite-state systems, namely discrete linear dynamical systems. While such systems are ubiquitous in mathematics, physics, engineering, etc., in the present context our motivation stems from their relevance to the formal analysis and verification of program loops, weighted automata, hybrid systems, and control systems, amongst many others. Our main object of study is the problem of model checking temporal properties on the infinite orbit of a linear dynamical system, and our principal contribution is to show that for a rich class of properties this problem can be reduced to certain classical decision problems on linear recurrence sequences, notably the Skolem Problem. This leads us to discuss recent advances on the latter and to highlight the prospects for further progress on charting the algorithmic landscape of linear recurrence sequences and linear dynamical systems
Algebraic Model Checking for Discrete Linear Dynamical Systems
Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass of infinite-state systems, namely discrete linear dynamical systems. While such systems are ubiquitous in mathematics, physics, engineering, etc., in the present context our motivation stems from their relevance to the formal analysis and verification of program loops, weighted automata, hybrid systems, and control systems, amongst many others. Our main object of study is the problem of model checking temporal properties on the infinite orbit of a linear dynamical system, and our principal contribution is to show that for a rich class of properties this problem can be reduced to certain classical decision problems on linear recurrence sequences, notably the Skolem Problem. This leads us to discuss recent advances on the latter and to highlight the prospects for further progress on charting the algorithmic landscape of linear recurrence sequences and linear dynamical systems
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