Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Deciding Reachability for Piecewise Constant Derivative Systems on Orientable Manifolds

© 2019 Springer-Verlag. This is a post-peer-review, pre-copyedit version of a paper published in Reachability Problems: 13th International Conference, RP 2019, Brussels, Belgium, September 11–13, 2019, Proceedings. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-030-30806-3_14A hybrid automaton is a finite state machine combined with some k real-valued continuous variables, where k determines the number of the automaton dimensions. This formalism is widely used for modelling safety-critical systems, and verification tasks for such systems can often be expressed as the reachability problem for hybrid automata. Asarin, Mysore, Pnueli and Schneider defined classes of hybrid automata lying on the boundary between decidability and undecidability in their seminal paper ‘Low dimensional hybrid systems - decidable, undecidable, don’t know’ [9]. They proved that certain decidable classes become undecidable when given a little additional computational power, and showed that the reachability question remains unsolved for some 2-dimensional systems. Piecewise Constant Derivative Systems on 2-dimensional manifolds (or PCD2m) constitute a class of hybrid automata for which decidability of the reachability problem is unknown. In this paper we show that the reachability problem becomes decidable for PCD2m if we slightly limit their dynamics, and thus we partially answer the open question of Asarin, Mysore, Pnueli and Schneider posed in [9]

Robust Analysis of Timed Automata via Channel Machines

International audienceWhereas formal verification of timed systems has become a very active field of research, the idealised mathematical semantics of timed automata cannot be faithfully implemented. Several works have thus focused on a modified semantics of timed automata which ensures implementability, and robust model-checking algorithms for safety, and later LTL properties have been designed. Recently, a~new approach has been proposed, which reduces (standard) model-checking of timed automata to other verification problems on channel machines. Thanks to a new encoding of the modified semantics as a network of timed systems, we propose an original combination of both approaches, and prove that robust model-checking for coFlat-MTL, a large fragment of~MTL, is EXPSPACE-Complete

From offline toward real-time: A hybrid systems model checking and CPS co-design approach for Medical Device Plug-andPlay (MDPnP

Abstract—Hybrid systems model checking is a great success in guaranteeing the safety of computerized control cyber-physical systems (CPS). However, when applying hybrid systems model checking to Medical Device Plug-and-Play (MDPnP) CPS, we encounter two challenges due to the complexity of human body: i) there are no good offline differential equation based models for many human body parameters; ii) the complexity of human body can result in many variables, complicating the system model. In an attempt to address the challenges, we propose to alter the traditional approach of offline hybrid systems model checking of time-unbounded (i.e., infinite-horizon, a.k.a., long-run) future behavior to online hybrid systems model checking of time-bounded (i.e., finite-horizon, a.k.a., short-run) future behavior. According to this proposal, online model checking runs as a real-time task to prevent faults. To meet the real-time requirements, certain design patterns must be followed, which brings up the co-design issue. We propose two sets of system co-design patterns for hard real-time and soft real-time respectively. To evaluate our proposals, a case study on laser tracheotomy MDPnP is carried out. The study shows the necessity of online model checking. Furthermore, test results based on real-world human subject trace show the feasibility and effectiveness of our proposed co-design.

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

Semantics and computation of the evolution of hybrid systems with ariadne

In this talk we will present material on the semantics, computability, and algorithms for the evolution of hybrid dynamical systems, and an overview of the tool Ariadne for verification of hybrid systems [1]. Hybrid systems are characterised by undergoing continuous evolution interspersed by discrete jumps. They exhibit all the complexities of finite automata, nonlinear dynamic systems and differential equations, and are extremely difficult to analyze. We will consider hybrid systems in which the continuous dynamics is given by a differential equation x = f(x), with discrete jumps x' = ri(x) which occur as soon as a guard condition gi(x) = 0 is activated. It is clear that the evolution of a hybrid system undergoes discontinuities, but since only continuous functions are computable, it is not clear to what extent, if any, it is possible to perform a rigorous analysis of a hybrid system. We will first show that we can define lower and upper semantics of evolution under which it is possible to compute reachable sets, and that away from discontinuity points (such as grazing or corner collision points), these semantics agree [2]. In order to perform reachability analysis, it is necessary to define the evolution over bounded initial sets of states. We show that this can be done using the operations of range, compose, flow and solve operations on functions. We will see that constrained image sets of the form {f(x) | x ? D | g(x) ? C}, are sufficient to express the evolution exactly, except for the case of degenerate (non-transverse) cross- ings [3]. The flow operation is the most computationally demanding, and we will give some details of the implementation and efficiency considerations [4]. We will give examples of reachability analysis in Ariadne, including electrical power converters and heating systems. Finally, we will outline some areas of active research, including differential inclusions [5] and modular reasoning

Why Propositional Quantification Makes Modal Logics on Trees Robustly Hard?

International audienceAdding propositional quantification to the modal logics K, T or S4 is known to lead to undecid-ability but CTL with propositional quantification under the tree semantics (QCTL t) admits a non-elementary Tower-complete satisfiability problem. We investigate the complexity of strict fragments of QCTL t as well as of the modal logic K with propositional quantification under the tree semantics. More specifically, we show that QCTL t restricted to the temporal operator EX is already Tower-hard, which is unexpected as EX can only enforce local properties. When QCTL t restricted to EX is interpreted on N-bounded trees for some N ≥ 2, we prove that the satisfiability problem is AExp pol-complete; AExp pol-hardness is established by reduction from a recently introduced tiling problem, instrumental for studying the model-checking problem for interval temporal logics. As consequences of our proof method, we prove Tower-hardness of QCTL t restricted to EF or to EXEF and of the well-known modal logics K, KD, GL, S4, K4 and D4, with propositional quantification under a semantics based on classes of trees

Mortality and Edge-to-Edge Reachability are Decidable on Surfaces

© 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM. This is an open access paper distributed under the Creative Commons Attribution License, to view a copy of the license, see: https://creativecommons.org/licenses/by/4.0/The mortality problem for a given dynamical system S consists of determining whether every trajectory of S eventually halts. In this work, we show that this problem is decidable for the class of piecewise constant derivative systems on two-dimensional manifolds, also called surfaces (). Two closely related open problems are point-to-point and edge-to-edge reachability for . Building on our technique to establish decidability of mortality for , we show that the edge-to-edge reachability problem for these systems is also decidable. In this way we solve the edge-to-edge reachability case of an open problem due to Asarin, Mysore, Pnueli and Schneider [4]. This implies that the interval-to-interval version of the classical open problem of reachability for regular piecewise affine maps (PAMs) is also decidable. In other words, point-to-point reachability for regular PAMs can be effectively approximated with arbitrarily precision