Personal narratives are stories authors construct to make meaning of their experiences.Style, the distinctive way authors use language to express themselves, is fundamental to how these narratives convey subjective experiences.Yet there is a lack of a formal framework for systematically analyzing these stylistic choices.We present a novel approach that formalizes style in personal narratives as patterns in the linguistic choices authors make when communicating subjective experiences.Our framework integrates three domains: functional linguistics establishes language as a system of meaningful choices, computer science provides methods for automatically extracting and analyzing sequential patterns, and these patterns are linked to psychological observations.Using language models, we automatically extract linguistic features such as processes, participants, and circumstances.We apply our framework to hundreds of dream narratives, including a case study on a war veteran with post-traumatic stress disorder.Analysis of his narratives uncovers distinctive patterns, particularly how verbal processes dominate over mental ones, illustrating the relationship between linguistic choices and psychological states.

Formal models are important for theory-building, enhancing the precision of predictions and promoting collaboration. Researchers have argued that there is a lack of formal models in psychology. We present an automata-based method to formalize psychological theories, i.e. to transform verbal theories into formal models. This approach leverages the tools of theoretical computer science for formal theory development, for verification, comparison, collaboration, and modularity. We exemplify our method on Lazarus and Folkman's theory of stress, showcasing a step-by-step modeling of the theory.

Workflow nets are a well-established variant of Petri nets for the modeling of process activities such as business processes. The standard correctness notion of workflow nets is soundness, which comes in several variants. Their decidability was shown decades ago, but their complexity was only identified recently. In this work, we are primarily interested in two popular variants: 1-soundness and generalised soundness.

Decisiveness of infinite Markov chains with respect to some (finite or infinite) target set of states is a key property that allows to compute the reachability probability of this set up to an arbitrary precision. Most of the existing works assume constant weights for defining the probability of a transition in the considered models. However numerous probabilistic modelings require the (dynamic) weight to also depend on the current state. So we introduce a dynamic probabilistic version of counter machine (pCM). After establishing that decisiveness is undecidable for pCMs even with constant weights, we study the decidability of decisiveness for subclasses of pCM. We show that, without restrictions on dynamic weights, decisiveness is undecidable with a single state and single counter pCM. On the contrary with polynomial weights, decisiveness becomes decidable for single counter pCMs under mild conditions. Then we show that decisiveness of probabilistic Petri nets (pPNs) with polynomial weights is undecidable even when the target set is upward-closed unlike the case of constant weights. Finally we prove that the standard subclass of pPNs with a regular language is decisive with respect to a finite set whatever the kind of weights.

Bounding the number of reversals in a counter machine is one of the most prominent restrictions to achieve decidability of the reachability problem. Given this success, we explore whether this notion can be relaxed while retaining decidability. To this end, we introduce the notion of an f-reversal-bounded counter machine for a monotone function f: ℕ → ℕ. In such a machine, every run of length n makes at most f(n) reversals. Our first main result is a dichotomy theorem: We show that for every monotone function f, one of the following holds: Either (i) f grows so slowly that every f-reversal bounded counter machine is already k-reversal bounded for some constant k or (ii) f belongs to Ω(log(n)) and reachability in f-reversal bounded counter machines is undecidable. This shows that classical reversal bounding already captures the decidable cases of f-reversal bounding for any monotone function f. The key technical ingredient is an analysis of the growth of small solutions of iterated compositions of Presburger-definable constraints. In our second contribution, we investigate whether imposing f-reversal boundedness improves the complexity of the reachability problem in vector addition systems with states (VASS). Here, we obtain an analogous dichotomy: We show that either (i) f grows so slowly that every f-reversal-bounded VASS is already k-reversal-bounded for some constant k or (ii) f belongs to Ω(n) and the reachability problem for f-reversal-bounded VASS remains Ackermann-complete. This result is proven using run amalgamation in VASS. Overall, our results imply that classical restriction of reversal boundedness is a robust one.

A system of communicating finite state machines is synchronizable if its send trace semantics, i.e.the set of sequences of sendings it can perform, is the same when its communications are FIFO asynchronous and when they are just rendez-vous synchronizations. This property was claimed to be decidable in several conference and journal papers for either mailboxes or peer-to-peer communications, thanks to a form of small model property. In this paper, we show that this small model property does not hold neither for mailbox communications, nor for peer-to-peer communications, therefore the decidability of synchronizability becomes an open question. We close this question for peer-to-peer communications, and we show that synchronizability is actually undecidable. We show that synchronizability is decidable if the topology of communications is an oriented ring. We also show that, in this case, synchronizability implies the absence of unspecified receptions and orphan messages, and the channel-recognizability of the reachability set.

Abstract This paper presents a property-directed approach to verifying recurrent neural networks (RNNs). To this end, we learn a deterministic finite automaton as a surrogate model from a given RNN using active automata learning. This model may then be analyzed using model checking as a verification technique. The term property-directed reflects the idea that our procedure is guided and controlled by the given property rather than performing the two steps separately. We show that this not only allows us to discover small counterexamples fast, but also to generalize them by pumping toward faulty flows hinting at the underlying error in the RNN. We also show that our method can be efficiently used for adversarial robustness certification of RNNs.

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are input-bounded (i.e. the sequence of messages sent through a particular channel belongs to a given bounded language). We prove, by reducing this model to a counter machine with restricted zero tests, that the rational-reachability problem (and by extension, control-state reachability, unboundedness, deadlock, etc.) is decidable. This class of machines subsumes input-letter-bounded machines, flat machines, linear FIFO nets, and monogeneous machines, for which some of these problems were already shown to be decidable. These theoretical results can form the foundations to build a tool to verify general FIFO machines based on the analysis of input-bounded machines.

Several notions of synchronizability of a message-passing system have been introduced in the literature. Roughly, a system is called synchronizable if every execution can be rescheduled so that it meets certain criteria, e.g., a channel bound. We provide a framework, based on MSO logic and (special) tree-width, that unifies existing definitions, explains their good properties, and allows one to easily derive other, more general definitions and decidability results for synchronizability.

In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.

We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether the numbers in the input are encoded in unary or binary. As a key underlying technical result, we show that, if a configuration is reachable, then there exists a witnessing path whose sequence of transitions is contained in a bounded language defined by a regular expression of pseudo-polynomially bounded length. This, in turn, enables us to prove that the lengths of minimal reachability witnesses are pseudo-polynomially bounded.

Abstract Downward closures of Petri net reachability sets can be finitely represented by their set of maximal elements called the minimal coverability set or Clover. Many properties (coverability, boundedness, ...) can be decided using Clover, in a time proportional to the size of Clover. So it is crucial to design algorithms that compute it efficiently. We present a simple modification of the original but incomplete Minimal Coverability Tree algorithm (MCT), computing Clover, which makes it complete: it memorizes accelerations and fires them as ordinary transitions. Contrary to the other alternative algorithms for which no bound on the size of the required additional memory is known, we establish that the additional space of our algorithm is at most doubly exponential. Furthermore we have implemented a prototype which is already very competitive: on benchmarks it uses less space than all the other tools and its execution time is close to the one of the fastest tool.

Abstract We define representations for downward-closed subsets of a rich family of well-quasi-orders, and more generally for closed subsets of an even richer family of Noetherian topological spaces. This includes the cases of finite words, of multisets, of finite trees, notably. Those representations are given as finite unions of ideals, or more generally of irreducible closed subsets. All the representations we explore are computable, in the sense that we exhibit algorithms that decide inclusion, and compute finite unions and finite intersections. The origin of this work lies in the need for computing finite representations of sets of successors of the downward closure of one state, or more generally of a downward-closed set of states, in a well-structured transition system, and this is where we start: we define adequate notions of completions of well-quasi-orders, and more generally, of Noetherian spaces. For verification purposes, we argue that the required completions must be ideal completions, or more generally sobrifications, that is, spaces of irreducible closed subsets.

The decidability and complexity of reachability problems and model-checking for flat counter systems have been explored in detail. However, only few results are known for flat FIFO systems, only in some particular cases (a single loop or a single bounded expression). We prove, by establishing reductions between properties, and by reducing SAT to a subset of these properties that many verification problems like reachability, non-termination, unboundedness are NP-complete for flat FIFO systems, generalizing similar existing results for flat counter systems. We construct a trace-flattable counter system that is bisimilar to a given flat FIFO system, which allows to model-check the original flat FIFO system. Our results lay the theoretical foundations and open the way to build a verification tool for (general) FIFO systems based on analysis of flat subsystems.

We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. However, the strong well structured problem is decidable for all Presburger counter machines. While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured problem for 1-Affine VASS.

We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000.

Abstract In this paper, we study the information system verification problem as a parameterized verification one. Informations systems are modeled as multi-parameterized systems in a formal language based on the Algebraic State-Transition Diagrams (ASTD) notation. Then, we use the Well Structured Transition Systems (WSTS) theory to solve the coverability problem for an unbounded ASTD state space. Moreover, we define a new framework to prove the effective pred-basis condition of WSTSs, i.e. the computability of a base of predecessors for every states.

The well-quasi-ordering (i.e., a well-founded quasi-ordering such that all antichains are finite) that defines well-structured transition systems (WSTS) is shown not to be the weakest hypothesis that implies decidability of the coverability problem. We show coverability decidable for monotone transition systems that only require the absence of infinite antichains and call well behaved transitions systems (WBTS) the new strict superclass of the class of WSTS that arises. By contrast, we confirm that boundedness and termination are undecidable for WBTS under the usual hypotheses, and show that stronger monotonicity conditions can enforce decidability. Proofs are similar or even identical to existing proofs but the surprising message is that a hypothesis implicitely assumed minimal for twenty years in the theory of WSTS can meaningfully be relaxed, allowing more orderings to be handled in an abstract way. Comment: 19 pages, 3 figures

Continuous Petri nets are a relaxation of classical discrete Petri nets in which transitions can be fired a fractional number of times, and consequently places may contain a fractional number of tokens. Such continuous Petri nets are an appealing object to study, since they over-approximate the set of reachable configurations of their discrete counterparts, and their reachability problem is known to be decidable in polynomial time. The starting point of this article is to show that the reachability relation for continuous Petri nets is definable by a sentence of linear size in the existential theory of the rationals with addition and order. Using this characterization, we obtain decidability and complexity results for a number of classical decision problems for continuous Petri nets. In particular, we settle the open problem about the precise complexity of reachability set inclusion. Finally, we show how continuous Petri nets can be incorporated inside the classical backward coverability algorithm for discrete Petri nets as a pruning heuristic to tackle the symbolic state explosion problem. The cornerstone of the approach we present is that our logical characterization enables us to leverage the power of modern SMT-solvers to yield a highly performant and robust decision procedure for coverability in Petri nets. We demonstrate the applicability of our approach on a set of standard benchmarks from the literature.

and extended versions of the papers selected from the 6th of the Reachability Problems Workshop hosted by the University of Bordeaux, France from 17 till

Known to be decidable since 1981, there still remains a huge gap between the best known lower and upper bounds for the reach ability problem for vector addition systems with states (VASS). Here the problem is shown PSPACE-complete in the two-dimensional case, vastly improving on the doubly exponential time bound established in 1986 by Howell, Rosier, Huynh and Yen. Cover ability and bounded ness for two-dimensional VASS are also shown PSPACE-complete, and reach ability in two-dimensional VASS and in integer VASS under unary encoding are considered.

We study the possibility of extending the Rackoff technique to Affine nets, which are Petri nets extended with affine functions. The Rackoff technique has been used for establishing EXPSPACE upper bounds for the coverability and boundedness problems for Petri nets. We show that this technique can be extended to strongly increasing Affine nets, obtaining better upper bounds compared to known results. The possible copies between places of a strongly increasing Affine net make this extension non-trivial. One cannot expect similar results for the entire class of Affine nets since coverability is Ackermann-hard and boundedness is undecidable. Moreover, it can be proved that model checking a logic expressing generalized coverability properties is undecidable for strongly increasing Affine nets, while it is known to be EXPSPACE-complete for Petri nets.

Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer cover, hybrid between the reachability and cover sets, reclaiming accuracy on one component. We show that this filtered cover is still recursive, but that equality of two such filtered covers, even for usual Vector Addition Systems (with no zero-test), is undecidable.

We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation.

We analyze the model-checking problems for safety and liveness properties in parameterized broadcast protocols. We show that the procedure suggested previously for safety properties may not terminate, whereas termination is guaranteed for the procedure based on upward closed sets. We show that the model-checking problem for liveness properties is undecidable. In fact, even the problem of deciding if a broadcast protocol may exhibit an infinite behavior is undecidable.

We consider the problem of verifying correctness of finite state machines that communicate with each other over unbounded FIFO channels that are unreliable. Various problems regarding verification of FIFO channels that can lose messages have been considered by Finkel [10], and by Abdulla and Johnson [1, 2]. We consider, in this paper, other possible unreliable behaviors of communication channels, viz. (a) duplication and (b) insertion errors. Furthermore, we also consider various combinations of duplication, insertion and lossiness errors.Finite state machines that communicate over unbounded FIFO buffers is a model of computation that forms the backbone of ISO standard protocol specification languages Estelle and SDL. While an assumption of a perfect communication medium is reasonable at the higher levels of the OSI protocol stack, the lower levels have to deal with an unreliable communication medium; hence our motivation for the present work.The verification problems that are of interest are reachability, unboundedness, deadlock, and model-checking against CTL. All of these problems are undecidable for machines communicating over reliable unbounded FIFO channels. So, it is perhaps surprising that some of these problems become decidable when unreliable channels are modeled. The contributions of this paper are: (a) An investigation of solutions to these problems for machines with insertion errors, duplication errors, or a combination of duplication, insertion and lossiness errors, and (b) A comparison of the relative expressive power of the various errors.