4,428 research outputs found
MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs
Randomized Non-sequential Processes and Distributed Adversaries
We suggest a non-sequential, i.e., partial-order, semantics for randomized distributed algorithms. It is based on Petri nets and their branching processes. We introduce randomized Petri nets and their semantics probabilistic branching processes. As a main result, we show that each probabilistic branching process defines a unique canonical probability space on the set of its maximal runs. Finally, we show that the non-sequential semantics differs from the classical sequential semantics, modelling a new adversary, called the distributed adversary
Transforming nested structures of flowchart into hierarchical coloured Petri Nets
Flowchart is commonly used diagram to represent the processes in design phase of a software system. However, the flowchart of a complex software system inevitably contains the nested structures of branching and looping of the processes. The verification of these nested structure of the flowchart in advance is still difficult to conduct even using simulation techniques. In this paper, we intend to consider the complex flowchart with nested structures, so called nested-if and nested-loop, as our input design model. A set of mapping rules is proposed to transform the input complex flowchart with nested structures into the hierarchical coloured Petri nets to avoid the drawing of a single huge net of complicate model. The hierarchical coloured Petri nets also provides us to manage level of abstraction of the formal model and helps us concentrate on only an appropriate detail at a time. In our transforming approach, both data flow and control flow of the processes in flowchart are concerned as well so that all changing states of the observable variables in the flowchart would be represented and simulated in our resulting hierarchical coloured Petri nets. The CPN simulation tool is used to test and ensure the correctness of our resulting hierarchical coloured Petri nets
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
Branching cells as local states for event structures and nets: probabilistic applications
International audienceWe study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. We propose a construction for probabilities over so-called locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state
Finite petri nets as models for recursive causal behaviour
Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud
\ud
B=(a.nilb.B)+c.nil. \ud
\ud
We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence
Petri Games: Synthesis of Distributed Systems with Causal Memory
We present a new multiplayer game model for the interaction and the flow of
information in a distributed system. The players are tokens on a Petri net. As
long as the players move in independent parts of the net, they do not know of
each other; when they synchronize at a joint transition, each player gets
informed of the causal history of the other player. We show that for Petri
games with a single environment player and an arbitrary bounded number of
system players, deciding the existence of a safety strategy for the system
players is EXPTIME-complete.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Distributed Non-Interference
Information flow security properties were defined some years ago (see, e.g.,
the surveys \cite{FG01,Ry01}) in terms of suitable equivalence checking
problems. These definitions were provided by using sequential models of
computations (e.g., labeled transition systems \cite{GV15}), and interleaving
behavioral equivalences (e.g., bisimulation equivalence \cite{Mil89}). More
recently, the distributed model of Petri nets has been used to study
non-interference in \cite{BG03,BG09,BC15}, but also in these papers an
interleaving semantics was used. We argue that in order to capture all the
relevant information flows, truly-concurrent behavioral equivalences must be
used. In particular, we propose for Petri nets the distributed non-interference
property, called DNI, based on {\em branching place bisimilarity}
\cite{Gor21b}, which is a sensible, decidable equivalence for finite Petri nets
with silent moves. Then we focus our attention on the subclass of Petri nets
called {\em finite-state machines}, which can be represented (up to
isomorphism) by the simple process algebra CFM \cite{Gor17}. DNI is very easily
checkable on CFM processes, as it is compositional, so that it does does not
suffer from the state-space explosion problem. Moreover, we show that DNI can
be characterized syntactically on CFM by means of a type system
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
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