2,304 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 Kosarajuâs 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
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Computer-aided analysis of concurrent systems
The introduction of concurrency into programs has added to the complexity of the software design process. This is most evident in the design of communications protocols where concurrency is inherent to the behavior of the system. The complexity exhibited by such software systems makes more evident the needs for computer-aided tools for automatically analyzing behavior.The Distributed Systems project at UCI has been developing a suite of tools, based on Petri nets, which support the design and evaluation of concurrent software systems. This paper focuses attention on one of the tools: the reachability graph analyzer (RGA). This tool provides mechanisms for proving general system properties (e.g., deadlock-freeness) as well as system-specific properties. The tool is sufficiently general to allow a user to apply complex user-defined analysis algorithms to reachability graphs. The alternating-bit protocol with a bounded channel is used to demonstrate the power of the tool and to point to future extensions
Algorithmic Verification of Asynchronous Programs
Asynchronous programming is a ubiquitous systems programming idiom to manage
concurrent interactions with the environment. In this style, instead of waiting
for time-consuming operations to complete, the programmer makes a non-blocking
call to the operation and posts a callback task to a task buffer that is
executed later when the time-consuming operation completes. A co-operative
scheduler mediates the interaction by picking and executing callback tasks from
the task buffer to completion (and these callbacks can post further callbacks
to be executed later). Writing correct asynchronous programs is hard because
the use of callbacks, while efficient, obscures program control flow.
We provide a formal model underlying asynchronous programs and study
verification problems for this model. We show that the safety verification
problem for finite-data asynchronous programs is expspace-complete. We show
that liveness verification for finite-data asynchronous programs is decidable
and polynomial-time equivalent to Petri Net reachability. Decidability is not
obvious, since even if the data is finite-state, asynchronous programs
constitute infinite-state transition systems: both the program stack and the
task buffer of pending asynchronous calls can be potentially unbounded.
Our main technical construction is a polynomial-time semantics-preserving
reduction from asynchronous programs to Petri Nets and conversely. The
reduction allows the use of algorithmic techniques on Petri Nets to the
verification of asynchronous programs.
We also study several extensions to the basic models of asynchronous programs
that are inspired by additional capabilities provided by implementations of
asynchronous libraries, and classify the decidability and undecidability of
verification questions on these extensions.Comment: 46 pages, 9 figure
Bounded LTL Model Checking with Stable Models
In this paper bounded model checking of asynchronous concurrent systems is
introduced as a promising application area for answer set programming. As the
model of asynchronous systems a generalisation of communicating automata,
1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a
requirement on the behaviour of the net can be translated into a logic program
such that the bounded model checking problem for the net can be solved by
computing stable models of the corresponding program. The use of the stable
model semantics leads to compact encodings of bounded reachability and deadlock
detection tasks as well as the more general problem of bounded model checking
of linear temporal logic. Correctness proofs of the devised translations are
given, and some experimental results using the translation and the Smodels
system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin
Ranking Functions for Vector Addition Systems
Vector addition systems are an important model in theoretical computer
science and have been used for the analysis of systems in a variety of areas.
Termination is a crucial property of vector addition systems and has received
considerable interest in the literature. In this paper we give a complete
method for the construction of ranking functions for vector addition systems
with states. The interest in ranking functions is motivated by the fact that
ranking functions provide valuable additional information in case of
termination: They provide an explanation for the progress of the vector
addition system, which can be reported to the user of a verification tool, and
can be used as certificates for termination. Moreover, we show how ranking
functions can be used for the computational complexity analysis of vector
addition systems (here complexity refers to the number of steps the vector
addition system under analysis can take in terms of the given initial vector)
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes
We propose a framework for reasoning about unbounded dynamic networks of
infinite-state processes. We propose Constrained Petri Nets (CPN) as generic
models for these networks. They can be seen as Petri nets where tokens
(representing occurrences of processes) are colored by values over some
potentially infinite data domain such as integers, reals, etc. Furthermore, we
define a logic, called CML (colored markings logic), for the description of CPN
configurations. CML is a first-order logic over tokens allowing to reason about
their locations and their colors. Both CPNs and CML are parametrized by a color
logic allowing to express constraints on the colors (data) associated with
tokens. We investigate the decidability of the satisfiability problem of CML
and its applications in the verification of CPNs. We identify a fragment of CML
for which the satisfiability problem is decidable (whenever it is the case for
the underlying color logic), and which is closed under the computations of post
and pre images for CPNs. These results can be used for several kinds of
analysis such as invariance checking, pre-post condition reasoning, and bounded
reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published
in the the Proceedings of TACAS 2007, LNCS 442
The Reachability Problem for Petri Nets is Not Elementary
Petri nets, also known as vector addition systems, are a long established
model of concurrency with extensive applications in modelling and analysis of
hardware, software and database systems, as well as chemical, biological and
business processes. The central algorithmic problem for Petri nets is
reachability: whether from the given initial configuration there exists a
sequence of valid execution steps that reaches the given final configuration.
The complexity of the problem has remained unsettled since the 1960s, and it is
one of the most prominent open questions in the theory of verification.
Decidability was proved by Mayr in his seminal STOC 1981 work, and the
currently best published upper bound is non-primitive recursive Ackermannian of
Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound,
i.e. that the reachability problem needs a tower of exponentials of time and
space. Until this work, the best lower bound has been exponential space, due to
Lipton in 1976. The new lower bound is a major breakthrough for several
reasons. Firstly, it shows that the reachability problem is much harder than
the coverability (i.e., state reachability) problem, which is also ubiquitous
but has been known to be complete for exponential space since the late 1970s.
Secondly, it implies that a plethora of problems from formal languages, logic,
concurrent systems, process calculi and other areas, that are known to admit
reductions from the Petri nets reachability problem, are also not elementary.
Thirdly, it makes obsolete the currently best lower bounds for the reachability
problems for two key extensions of Petri nets: with branching and with a
pushdown stack.Comment: Final version of STOC'1
Dependability Analysis of Control Systems using SystemC and Statistical Model Checking
Stochastic Petri nets are commonly used for modeling distributed systems in
order to study their performance and dependability. This paper proposes a
realization of stochastic Petri nets in SystemC for modeling large embedded
control systems. Then statistical model checking is used to analyze the
dependability of the constructed model. Our verification framework allows users
to express a wide range of useful properties to be verified which is
illustrated through a case study
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