Parameterized Model Checking of Token-Passing Systems

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed $\textsf{CTL}^\ast \backslash \textsf{X}$. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ in uni-directional token rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et al. (2004) have shown a similar result for general topologies and indexed $\textsf{LTL} \backslash \textsf{X}$, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is cleare

Parameterized Model-Checking for Timed-Systems with Conjunctive Guards (Extended Version)

In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an \emph{apriori} unknown number of Timed Automata instantiated from a finite set $U_1, \dots, U_n$ of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions

An interval logic for higher-level temporal reasoning

Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included

Logical methods for the hierarchy of hyperlogics

In this thesis, we develop logical methods for reasoning about hyperproperties. Hyperproperties describe relations between multiple executions of a system. Unlike trace properties, hyperproperties comprise relational properties like noninterference, symmetry, and robustness. While trace properties have been studied extensively, hyperproperties form a relatively new concept that is far from fully understood. We study the expressiveness of various hyperlogics and develop algorithms for their satisfiability and synthesis problems. In the first part, we explore the landscape of hyperlogics based on temporal logics, first-order and second-order logics, and logics with team semantics. We establish that first-order/second-order and temporal hyperlogics span a hierarchy of expressiveness, whereas team logics constitute a radically different way of specifying hyperproperties. Furthermore, we introduce the notion of temporal safety and liveness, from which we obtain fragments of HyperLTL (the most prominent hyperlogic) with a simpler satisfiability problem. In the second part, we develop logics and algorithms for the synthesis of smart contracts. We introduce two extensions of temporal stream logic to express (hyper)properties of infinite-state systems. We study the realizability problem of these logics and define approximations of the problem in LTL and HyperLTL. Based on these approximations, we develop algorithms to construct smart contracts directly from their specifications.In dieser Arbeit beschreiben wir logische Methoden, um über Hypereigenschaften zu argumentieren. Hypereigenschaften beschreiben Relationen zwischen mehreren Ausführungen eines Systems. Anders als pfadbasierte Eigenschaften können Hypereigenschaften relationale Eigenschaften wie Symmetrie, Robustheit und die Abwesenheit von Informationsfluss ausdrücken. Während pfadbasierte Eigenschaften in den letzten Jahrzehnten ausführlich erforscht wurden, sind Hypereigenschaften ein relativ neues Konzept, das wir noch nicht vollständig verstehen. Wir untersuchen die Ausdrucksmächtigkeit verschiedener Hyperlogiken und entwickeln ausführbare Algorithmen, um deren Erfüllbarkeits- und Syntheseproblem zu lösen. Im ersten Teil erforschen wir die Landschaft der Hyperlogiken basierend auf temporalen Logiken, Logiken erster und zweiter Ordnung und Logiken mit Teamsemantik. Wir stellen fest, dass temporale Logiken und Logiken erster und zweiter Ordnung eine Hierarchie an Ausdrucksmächtigkeit aufspannen. Teamlogiken hingegen spezifieren Hypereigenschaften auf eine radikal andere Art. Wir führen außerdem das Konzept von temporalen Sicherheits- und Lebendigkeitseigenschaften ein, durch die Fragmente der bedeutensten Logik HyperLTL entstehen, für die das Erfüllbarkeitsproblem einfacher ist. Im zweiten Teil entwickeln wir Logiken und Algorithmen für die Synthese digitaler Verträge. Wir führen zwei Erweiterungen temporaler Stromlogik ein, um (Hyper)eigenschaften in unendlichen Systemen auszudrücken. Wir untersuchen das Realisierungsproblem dieser Logiken und definieren Approximationen des Problems in LTL und HyperLTL. Basierend auf diesen Approximationen entwickeln wir Algorithmen, die digitale Verträge direkt aus einer Spezifikation erstellen

Visibly Pushdown Modular Games

Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is local to a module and is oblivious to previous module invocations, and thus does not depend on the context of invocation. In this work, we study for the first time modular strategies with respect to winning conditions that can be expressed by a pushdown automaton. We show that such games are undecidable in general, and become decidable for visibly pushdown automata specifications. Our solution relies on a reduction to modular games with finite-state automata winning conditions, which are known in the literature. We carefully characterize the computational complexity of the considered decision problem. In particular, we show that modular games with a universal Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and when the winning condition is given by a CARET or NWTL temporal logic formula the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple fragments of these logics. As a further contribution, we present a different solution for modular games with finite-state automata winning condition that runs faster than known solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Benchmarks for Parity Games (extended version)

We propose a benchmark suite for parity games that includes all benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from https://github.com/jkeiren/paritygame-generator. This is an extended version of the paper that has been accepted for FSEN 201

Technical Report: Distribution Temporal Logic: Combining Correctness with Quality of Estimation

We present a new temporal logic called Distribution Temporal Logic (DTL) defined over predicates of belief states and hidden states of partially observable systems. DTL can express properties involving uncertainty and likelihood that cannot be described by existing logics. A co-safe formulation of DTL is defined and algorithmic procedures are given for monitoring executions of a partially observable Markov decision process with respect to such formulae. A simulation case study of a rescue robotics application outlines our approach.Comment: More expanded version of "Distribution Temporal Logic: Combining Correctness with Quality of Estimation" to appear in IEEE CDC 201