Theorem Proving for Pointwise Metric Temporal Logic Over the Naturals via Translations

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Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains

In this paper we look into the problem of planning over hybrid domains, where change can be both discrete and instantaneous, or continuous over time. In addition, it is required that each state on the trajectory induced by the execution of plans complies with a given set of global constraints. We approach the computation of plans for such domains as the problem of searching over a deterministic state model. In this model, some of the successor states are obtained by solving numerically the so-called initial value problem over a set of ordinary differential equations (ODE) given by the current plan prefix. These equations hold over time intervals whose duration is determined dynamically, according to whether zero crossing events take place for a set of invariant conditions. The resulting planner, FS+, incorporates these features together with effective heuristic guidance. FS+ does not impose any of the syntactic restrictions on process effects often found on the existing literature on Hybrid Planning. A key concept of our approach is that a clear separation is struck between planning and simulation time steps. The former is the time allowed to observe the evolution of a given dynamical system before committing to a future course of action, whilst the later is part of the model of the environment. FS+ is shown to be a robust planner over a diverse set of hybrid domains, taken from the existing literature on hybrid planning and systems.Comment: 17 page

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automaticallyverifying complex systems. Recently, model checkers have appearedin computer tools for the analysis of biochemical (and generegulatory) networks. We survey several such tools to assess thepotential of model checking in computational biology. Next, our overviewfocuses on direct applications of existing model checkers, as well ason algorithms for biochemical network analysis influenced by modelchecking, such as those using binary decision diagrams or Booleansatisfiability solvers. We conclude with advantages and drawbacks ofmodel checking for the analysis of biochemical networks

Petri Net Reachability Graphs: Decidability Status of FO Properties

We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order, modal and pattern-based languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques

The Interval Domain: A Matchmaker for aCTL and aPCTL

AbstractWe present aPCTL, a version of PCTL with an action-based semantics which coincides with the ordinary PCTL in case of a sole action type. We point out what aspects of aPCTL may be improved for its application as a probabilistic logic in a tool modeling large probabilistic system. We give a non-standard semantics to the action-based temporal logical aCTL, where the propositional clauses are interpreted in a fuzzy and the modalities in a probabilistic way; the until-construct is evaluated as a least fixed-point over these meanings. We view aCTL formulas ⊘ as templates for aPCTL formulas (which still need vectors of thresholds as annotations for all subformulas which are path formulas). Since [⊘]s, our non-standard meaning of ø at state s, is an interval [a, b], we may craft aPCTL formulas ø from using the information a and b respectively. This results in two aPCTL formulas ø and ø1. This translation defines a critical region of such thresholds for ⊘ in the following sense: if a > 0 then a satisfies the aPCTL formula ø1 dually, if b < 1 then s does not satisfy the formula ø1. Thus, any interesting probabilistic dynamics of aPCTL formulas with “pattern” ⊘ has to happen within the n-dimensional interval determined by out non-standard aCTL semantics [⊘].we would like to thank Martín Hötzel Escardó for suggesting to look at the interval domain at the LICS'97 meeting in Warsaw. He also pointed to work in his PhD thesis about the universality of I. we also acknowledge Marta Kwaitkowska, Christel Baier, Rance Cleaveland, and Scott Smolka for fruitful discussion on this subject matter

Linear-Time Temporal Logic with Team Semantics : Expressivity and Complexity

Peer reviewe

Logical and deep learning methods for temporal reasoning

In this thesis, we study logical and deep learning methods for the temporal reasoning of reactive systems. In Part I, we determine decidability borders for the satisfiability and realizability problem of temporal hyperproperties. Temporal hyperproperties relate multiple computation traces to each other and are expressed in a temporal hyperlogic. In particular, we identify decidable fragments of the highly expressive hyperlogics HyperQPTL and HyperCTL*. As an application, we elaborate on an enforcement mechanism for temporal hyperproperties. We study explicit enforcement algorithms for specifications given as formulas in universally quantified HyperLTL. In Part II, we train a (deep) neural network on the trace generation and realizability problem of linear-time temporal logic (LTL). We consider a method to generate large amounts of additional training data from practical specification patterns. The training data is generated with classical solvers, which provide one of many possible solutions to each formula. We demonstrate that it is sufficient to train on those particular solutions such that the neural network generalizes to the semantics of the logic. The neural network can predict solutions even for formulas from benchmarks from the literature on which the classical solver timed out. Additionally, we show that it solves a significant portion of problems from the annual synthesis competition (SYNTCOMP) and even out-of-distribution examples from a recent case study.Diese Arbeit befasst sich mit logischen Methoden und mehrschichtigen Lernmethoden für das zeitabhängige Argumentieren über reaktive Systeme. In Teil I werden die Grenzen der Entscheidbarkeit des Erfüllbarkeits- und des Realisierbarkeitsproblem von temporalen Hypereigenschaften bestimmt. Temporale Hypereigenschaften setzen mehrere Berechnungsspuren zueinander in Beziehung und werden in einer temporalen Hyperlogik ausgedrückt. Insbesondere werden entscheidbare Fragmente der hochexpressiven Hyperlogiken HyperQPTL und HyperCTL* identifiziert. Als Anwendung wird ein Enforcement-Mechanismus für temporale Hypereigenschaften erarbeitet. Explizite Enforcement-Algorithmen für Spezifikationen, die als Formeln in universell quantifiziertem HyperLTL angegeben werden, werden untersucht. In Teil II wird ein (mehrschichtiges) neuronales Netz auf den Problemen der Spurgenerierung und Realisierbarkeit von Linear-zeit Temporallogik (LTL) trainiert. Es wird eine Methode betrachtet, um aus praktischen Spezifikationsmustern große Mengen zusätzlicher Trainingsdaten zu generieren. Die Trainingsdaten werden mit klassischen Solvern generiert, die zu jeder Formel nur eine von vielen möglichen Lösungen liefern. Es wird gezeigt, dass es ausreichend ist, an diesen speziellen Lösungen zu trainieren, sodass das neuronale Netz zur Semantik der Logik generalisiert. Das neuronale Netz kann Lösungen sogar für Formeln aus Benchmarks aus der Literatur vorhersagen, bei denen der klassische Solver eine Zeitüberschreitung hatte. Zusätzlich wird gezeigt, dass das neuronale Netz einen erheblichen Teil der Probleme aus dem jährlichen Synthesewettbewerb (SYNTCOMP) und sogar Beispiele außerhalb der Distribution aus einer aktuellen Fallstudie lösen kann

Towards Physical Hybrid Systems

Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure zero sets have no tangible physical effect in a real system. We develop the concept of "physical hybrid systems" (PHS) to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of PHS.Comment: CADE 201