We define extensions of CTL and TCTL with strategic operators, called Strategic CTL (SCTL) and Strategic TCTL (STCTL), respectively. For each of the above logics we give a synchronous and asynchronous semantics, ie STCTL is interpreted over networks of extended Timed Automata (TA) that either make synchronous moves or synchronise via joint actions. We consider several semantics regarding information: imperfect (i) and perfect (I), and recall: imperfect (r) and perfect (R). We prove that SCTL is more expressive than ATL for all semantics, and this holds for the timed versions as well. Moreover, the model checking problem for STCTLir is of the same complexity as for ATLir, the model checking problem for STCTLir is of the same complexity as for TCTL, while for STCTLiR it is undecidable as for ATLiR. The above results suggest to use STCTLir and STCTLir in practical applications. Therefore, we use the tool IMITATOR to support model checking of STCTLir.

Strategic Timed CTL (STCTL) is an expressive logic that integrates branching time CTL with the representation of continuous time, and the notion of strategic abilities of agents. This makes STCTL suitable for specifying properties of asynchronous multi-agent systems modeled as networks of Parametric Timed Automata (PTA). Existing model checkers and synthesis procedures for STCTL are often limited in scope (bounded analyses), rely on ad-hoc implementations, and are difficult to prove correct. In this paper we propose declarative methods for STCTL model checking and synthesis using rewriting logic. Our approach uses rewriting modulo SMT to represent clock constraints and timed parameters as terms in a rewrite theory, and we adequately capture the continuous semantics of STCTL via rewriting strategies. The resulting algebraic specification is executable in the rewrite engine Maude. This is a novel application of Maude’s strategy language and, since our procedures are grounded on logical means, it is simpler to prove them correct. Our approach advances the state of the art for the analysis of multi-agent systems by allowing for the nesting of temporal operators and universal STCTL formulas, which have not been considered before. We benchmark our rewrite theory against existing procedures for STCTL, demonstrating competitive performance and even outperforming dedicated procedures for the existential fragment of STCTL. We thus provide a more robust and verifiable approach to STCTL model checking and synthesis.

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the “standard” semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude—including full LTL model checking, analysis with user-defined execution strategies, and even statistical model checking—for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Roméo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Roméo in many cases.

Expressing attack-defence trees in a multiagent setting allows for studying a new aspect of security scenarios, namely, how the number of agents and their task assignment impact the performance,e.g.,attack time, of strategies executed by opposing coalitions. Optimal scheduling of agents' actions, a nontrivial problem, is thus vital. We discuss associated caveats and propose an algorithm that synthesizes such an assignment, targeting minimal attack time and using the minimal number of agents for a given attack-defence tree. We also investigate an alternative approach for the same problem using rewriting logic, starting with a simple and elegant declarative model, whose correctness (in terms of schedule's optimality) is self-evident. We then refine this specification, inspired by the design of our specialized algorithm, to obtain an efficient system that can be used as a playground to explore various aspects of attack-defence trees. We compare the two approaches on different benchmarks.

Expressing attack-defence trees in a multi-agent setting allows for studying a new aspect of security scenarios, namely how the number of agents and their task assignment impact the performance, e.g. attack time, of strategies executed by opposing coalitions. Optimal scheduling of agents' actions, a non-trivial problem, is thus vital. We discuss associated caveats and propose an algorithm that synthesises such an assignment, targeting minimal attack time and using minimal number of agents for a given attack-defence tree.

Abstract We study semi-algorithms to synthesise the constraints under which a Parametric Timed Automaton satisfies some liveness requirement. The algorithms traverse a possibly infinite parametric zone graph, searching for accepting cycles. We provide new search and pruning algorithms, leading to successful termination for many examples. We demonstrate the success and efficiency of these algorithms on a benchmark. We also illustrate parameter synthesis for the classical Bounded Retransmission Protocol. Finally, we introduce a new notion of completeness in the limit, to investigate if an algorithm enumerates all solutions.