Satisfiability Games for Branching-Time Logics

The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly exponential time, CTL is complete for single exponential time. Some decision procedures for these logics are known; they use tree automata, tableaux or axiom systems. In this paper we present a uniform game-theoretic framework for the satisfiability problem of these branching-time temporal logics. We define satisfiability games for the full branching-time temporal logic CTL* using a high-level definition of winning condition that captures the essence of well-foundedness of least fixpoint unfoldings. These winning conditions form formal languages of \omega-words. We analyse which kinds of deterministic {\omega}-automata are needed in which case in order to recognise these languages. We then obtain a reduction to the problem of solving parity or B\"uchi games. The worst-case complexity of the obtained algorithms matches the known lower bounds for these logics. This approach provides a uniform, yet complexity-theoretically optimal treatment of satisfiability for branching-time temporal logics. It separates the use of temporal logic machinery from the use of automata thus preserving a syntactical relationship between the input formula and the object that represents satisfiability, i.e. a winning strategy in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner closure of the input formula only. Last but not least, the games presented here come with an attempt at providing tool support for the satisfiability problem of complex branching-time logics like CTL* and CTL+

Verification of Branching-Time and Alternating-Time Properties for Exogenous Coordination Models

Information and communication systems enter an increasing number of areas of daily lives. Our reliance and dependence on the functioning of such systems is rapidly growing together with the costs and the impact of system failures. At the same time the complexity of hardware and software systems extends to new limits as modern hardware architectures become more and more parallel, dynamic and heterogenous. These trends demand for a closer integration of formal methods and system engineering to show the correctness of complex systems within the design phase of large projects. The goal of this thesis is to introduce a formal holistic approach for modeling, analysis and synthesis of parallel systems that potentially addresses complex system behavior at any layer of the hardware/software stack. Due to the complexity of modern hardware and software systems, we aim to have a hierarchical modeling framework that allows to specify the behavior of a parallel system at various levels of abstraction and that facilitates designing complex systems in an iterative refinement procedure, in which more detailed behavior is added successively to the system description. In this context, the major challenge is to provide modeling formalisms that are expressive enough to address all of the above issues and are at the same time amenable to the application of formal methods for proving that the system behavior conforms to its specification. In particular, we are interested in specification formalisms that allow to apply formal verification techniques such that the underlying model checking problems are still decidable within reasonable time and space bounds. The presented work relies on an exogenous modeling approach that allows a clear separation of coordination and computation and provides an operational semantic model where formal methods such as model checking are well suited and applicable. The channel-based exogenous coordination language Reo is used as modeling formalism as it supports hierarchical modeling in an iterative top-down refinement procedure. It facilitates reusability, exchangeability, and heterogeneity of components and forms the basis to apply formal verification methods. At the same time Reo has a clear formal semantics based on automata, which serve as foundation to apply formal methods such as model checking. In this thesis new modeling languages are presented that allow specifying complex systems in terms of Reo and automata models which yield the basis for a holistic approach on modeling, verification and synthesis of parallel systems. The second main contribution of this thesis are tailored branching-time and alternating time temporal logics as well as corresponding model checking algorithms. The thesis includes results on the theoretical complexity of the underlying model checking problems as well as practical results. For the latter the presented approach has been implemented in the symbolic verification tool set Vereofy. The implementation within Vereofy and evaluation of the branching-time and alternating-time model checker is the third main contribution of this thesis

Analysing oscillatory trends of discrete-state stochastic processes through HASL statistical model checking

The application of formal methods to the analysis of stochastic oscillators has been at the focus of several research works in recent times. In this paper we provide insights on the application of an expressive temporal logic formalism, namely the Hybrid Automata Stochastic Logic (HASL), to that issue. We show how one can take advantage of the expressive power of the HASL logic to define and assess relevant characteristics of (stochastic) oscillators

Reasoning About Strategies: On the Model-Checking Problem

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL\star, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent concurrent games. We prove that SL includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NonElementarySpace-hard. This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of obtaining an elementary model-checking problem. Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time. About these logics, we prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not harder than the one for ATL\star