331 research outputs found
KReach : a tool for reachability in petri nets
We present KReach, a tool for deciding reachability in general Petri nets. The tool is a full implementation of Kosaraju’s original 1982 decision procedure for reachability in VASS. We believe this to be the first implementation of its kind. We include a comprehensive suite of libraries for development with Vector Addition Systems (with States) in the Haskell programming language. KReach serves as a practical tool, and acts as an effective teaching aid for the theory behind the algorithm. Preliminary tests suggest that there are some classes of Petri nets for which we can quickly show unreachability. In particular, using KReach for coverability problems, by reduction to reachability, is competitive even against state-of-the-art coverability checkers
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
The Ecce and Logen Partial Evaluators and their Web Interfaces
We present Ecce and Logen, two partial evaluators for Prolog using the online and offline approach respectively. We briefly present the foundations of these tools and discuss various applications. We also present new implementations of these tools, carried out in Ciao Prolog. In addition to a command-line interface new user-friendly web interfaces were developed. These enable non-expert users to specialise logic programs using a web browser, without the need for a local installation
Extensions to the CEGAR approach on Petri nets
Formal verification is becoming more prevalent and often compulsory in the safety-critical system and software development processes. Reachability analysis can provide information about safety and invariant properties of the developed system. However, checking the reachability is a computationally hard problem, especially in the case of asynchronous or infinite state systems. Petri nets are widely used for the modeling and verification of such systems. In this paper we examine a recently published approach for the reachability checking of Petri net markings. We give proofs concerning the completeness and the correctness properties of the algorithm, and we introduce algorithmic improvements. We also extend the algorithm to handle new classes of problems: submarking coverability and reachability of Petri nets with inhibitor arcs
A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets
Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net
model and several translations to networks of timed automata have been proposed
for this model. We present a direct, DBM-based algorithm for forward
reachability analysis of bounded TAPNs extended with transport arcs, inhibitor
arcs and age invariants. We also give a complete proof of its correctness,
including reduction techniques based on symmetries and extrapolation. Finally,
we augment the algorithm with a novel state-space reduction technique
introducing a monotonic ordering on markings and prove its soundness even in
the presence of monotonicity-breaking features like age invariants and
inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and
the experimental results document an encouraging performance compared to
verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587
Monus Semantics in Vector Addition Systems with States
Vector addition systems with states (VASS) are a popular model for concurrent systems. However, many decision problems have prohibitively high complexity. Therefore, it is sometimes useful to consider overapproximating semantics in which these problems can be decided more efficiently.
We study an overapproximation, called monus semantics, that slightly relaxes the semantics of decrements: A key property of a vector addition systems is that in order to decrement a counter, this counter must have a positive value. In contrast, our semantics allows decrements of zero-valued counters: If such a transition is executed, the counter just remains zero.
It turns out that if only a subset of transitions is used with monus semantics (and the others with classical semantics), then reachability is undecidable. However, we show that if monus semantics is used throughout, reachability remains decidable. In particular, we show that reachability for VASS with monus semantics is as hard as that of classical VASS (i.e. Ackermann-hard), while the zero-reachability and coverability are easier (i.e. EXPSPACE-complete and NP-complete, respectively). We provide a comprehensive account of the complexity of the general reachability problem, reachability of zero configurations, and coverability under monus semantics. We study these problems in general VASS, two-dimensional VASS, and one-dimensional VASS, with unary and binary counter updates
Monus semantics in vector addition systems with states
Vector addition systems with states (VASS) are a popular model for concurrent
systems. However, many decision problems have prohibitively high complexity.
Therefore, it is sometimes useful to consider overapproximating semantics in
which these problems can be decided more efficiently.
We study an overapproximation, called monus semantics, that slightly relaxes
the semantics of decrements: A key property of a vector addition systems is
that in order to decrement a counter, this counter must have a positive value.
In contrast, our semantics allows decrements of zero-valued counters: If such a
transition is executed, the counter just remains zero.
It turns out that if only a subset of transitions is used with monus
semantics (and the others with classical semantics), then reachability is
undecidable. However, we show that if monus semantics is used throughout,
reachability remains decidable. In particular, we show that reachability for
VASS with monus semantics is as hard as that of classical VASS (i.e.
Ackermann-hard), while the zero-reachability and coverability are easier (i.e.
EXPSPACE-complete and NP-complete, respectively). We provide a comprehensive
account of the complexity of the general reachability problem, reachability of
zero configurations, and coverability under monus semantics. We study these
problems in general VASS, two-dimensional VASS, and one-dimensional VASS, with
unary and binary counter updates
The Role of Coverage in Online Reinforcement Learning
Coverage conditions -- which assert that the data logging distribution
adequately covers the state space -- play a fundamental role in determining the
sample complexity of offline reinforcement learning. While such conditions
might seem irrelevant to online reinforcement learning at first glance, we
establish a new connection by showing -- somewhat surprisingly -- that the mere
existence of a data distribution with good coverage can enable sample-efficient
online RL. Concretely, we show that coverability -- that is, existence of a
data distribution that satisfies a ubiquitous coverage condition called
concentrability -- can be viewed as a structural property of the underlying
MDP, and can be exploited by standard algorithms for sample-efficient
exploration, even when the agent does not know said distribution. We complement
this result by proving that several weaker notions of coverage, despite being
sufficient for offline RL, are insufficient for online RL. We also show that
existing complexity measures for online RL, including Bellman rank and
Bellman-Eluder dimension, fail to optimally capture coverability, and propose a
new complexity measure, the sequential extrapolation coefficient, to provide a
unification
- …