Between quantum logic and concurrency

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Capacity Bounded Grammars and Petri Nets

A capacity bounded grammar is a grammar whose derivations are restricted by assigning a bound to the number of every nonterminal symbol in the sentential forms. In the paper the generative power and closure properties of capacity bounded grammars and their Petri net controlled counterparts are investigated

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

On Languages Accepted by P/T Systems Composed of joins

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow. Here we continue this line of research introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only of joins. Moreover, we investigate how J languages relate to other families of formal languages. In particular, we show that every J language can be accepted by a log n space-bounded non-deterministic Turing machine with a one-way read-only input. We also show that every J language has a semilinear Parikh map and that J languages and context-free languages (CFLs) are incomparable

Dense-Timed Petri Nets: Checking Zenoness, Token liveness and Boundedness

We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fire; time can pass and disable transitions). We consider the following verification problems for TPNs. (i) Zenoness: whether there exists a zeno-computation from a given marking, i.e., an infinite computation which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [Escrig et al.]. Furthermore, the related question if there exist arbitrarily fast computations from a given marking is also decidable. On the other hand, universal zenoness, i.e., the question if all infinite computations from a given marking are zeno, is undecidable. (ii) Token liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token. We show decidability of the problem by reducing it to the coverability problem, which is decidable for TPNs. (iii) Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings, and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.Comment: 61 pages, 18 figure

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin

Decision Problems for Petri Nets with Names

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, width-boundedness and depth-boundedness, that factorize boundedness. Width-boundedness has already been proven to be decidable. We prove here undecidability of depth-boundedness. Finally, we obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure

Unfolding-Based Process Discovery

This paper presents a novel technique for process discovery. In contrast to the current trend, which only considers an event log for discovering a process model, we assume two additional inputs: an independence relation on the set of logged activities, and a collection of negative traces. After deriving an intermediate net unfolding from them, we perform a controlled folding giving rise to a Petri net which contains both the input log and all independence-equivalent traces arising from it. Remarkably, the derived Petri net cannot execute any trace from the negative collection. The entire chain of transformations is fully automated. A tool has been developed and experimental results are provided that witness the significance of the contribution of this paper.Comment: This is the unabridged version of a paper with the same title appearead at the proceedings of ATVA 201