Incremental, Inductive Coverability

We give an incremental, inductive (IC3) procedure to check coverability of well-structured transition systems. Our procedure generalizes the IC3 procedure for safety verification that has been successfully applied in finite-state hardware verification to infinite-state well-structured transition systems. We show that our procedure is sound, complete, and terminating for downward-finite well-structured transition systems---where each state has a finite number of states below it---a class that contains extensions of Petri nets, broadcast protocols, and lossy channel systems. We have implemented our algorithm for checking coverability of Petri nets. We describe how the algorithm can be efficiently implemented without the use of SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is competitive with state-of-the-art implementations for coverability based on symbolic backward analysis or expand-enlarge-and-check algorithms both in time taken and space usage.Comment: Non-reviewed version, original version submitted to CAV 2013; this is a revised version, containing more experimental results and some correction

Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

Well Structured Transition Systems with History

We propose a formal model of concurrent systems in which the history of a computation is explicitly represented as a collection of events that provide a view of a sequence of configurations. In our model events generated by transitions become part of the system configurations leading to operational semantics with historical data. This model allows us to formalize what is usually done in symbolic verification algorithms. Indeed, search algorithms often use meta-information, e.g., names of fired transitions, selected processes, etc., to reconstruct (error) traces from symbolic state exploration. The other interesting point of the proposed model is related to a possible new application of the theory of well-structured transition systems (wsts). In our setting wsts theory can be applied to formally extend the class of properties that can be verified using coverability to take into consideration (ordered and unordered) historical data. This can be done by using different types of representation of collections of events and by combining them with wsts by using closure properties of well-quasi orderings.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

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

Verification of soundness and other properties of business processes

In this thesis we focus on improving current modeling and verification techniques for complex business processes. The objective of the thesis is to consider several aspects of real-life business processes and give specific solutions to cope with their complexity. In particular, we address verification of a proper termination property for workflows, called generalized soundness. We give a new decision procedure for generalized soundness that improves the original decision procedure. The new decision procedure reports on the decidability status of generalized soundness and returns a counterexample in case the workflow net is not generalized sound. We report on experimental results obtained with the prototype implementation we made and describe how to verify large workflows compositionally, using reduction rules. Next, we concentrate on modeling and verification of adaptive workflows — workflows that are able to change their structure at runtime, for instance when some exceptional events occur. In order to model the exception handling properly and allow structural changes of the system in a modular way, we introduce a new class of nets, called adaptive workflow nets. Adaptive workflow nets are a special type of Nets in Nets and they allow for creation, deletion and transformation of net tokens at runtime and for two types of synchronizations: synchronization on proper termination and synchronization on exception. We define some behavioral properties of adaptive workflow nets: soundness and circumspectness and employ an abstraction to reduce the verification of these properties to the verification of behavioral properties of a finite state abstraction. Further, we study how formal methods can help in understanding and designing business processes. We investigate this for the extended event-driven process chains (eEPCs), a popular industrial business process language used in the ARIS Toolset. Several semantics have been proposed for EPCs. However, most of them concentrated solely on the control flow. We argue that other aspects of business processes must also be taken into account in order to analyze eEPCs and propose a semantics that takes data and time information from eEPCs into account. Moreover, we provide a translation of eEPCs to Timed Colored Petri nets in order to facilitate verification of eEPCs. Finally, we discuss modeling issues for business processes whose behavior may depend on the previous behavior of the process, history which is recorded by workflow management systems as a log. To increase the precision of models with respect to modeling choices depending on the process history, we introduce history-dependent guards. The obtained business processes are called historydependent processes.We introduce a logic, called LogLogics for the specification of guards based on a log of a current running process and give an evaluation algorithm for such guards. Moreover, we show how these guards can be used in practice and define LogLogics patterns for properties that occur most commonly in practice

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611