Structural liveness of Petri nets is ExpSpace-hard and decidable

It is more difficult to model a discrete system than a continuous system. Recently, a great number of applications of Petri nets to the design and the analysis of discrete systems has been reported. However, a common problem in its applications is that the required computer memories and the computation times increase explosively in accordance with the increase in the number of systems components. Some methods to divide or to reduce Petri nets have been proposed to solve this problem. Although the liveness and boundedness of Petri nets are held in the divided or reduced Petri nets, the reachability problem cannot be solved by these methods.This paper proposes another method to model discrete systems by Petri nets with place invariants. A sequential control system will be described as a typical kind of discrete system, and its structural characteristics will be used in modeling. Each component of a sequential control system will be modeled by a sub‐Petri net with place invariants. There are many components in one sequential control system, but not each one is necessarily complicated. Most sub‐Petri nets do not have so many places or transitions. It is also well known that a Petri net with place invariants is bounded and can be live by placing sufficient tokens into its initial marking. Besides, the reachability problem is not so difficult to solve in a small sub‐Petri net. Further, an activating relation to combine two or more sub‐Petri nets is defined, and some rules to reduce conflicts among enabled transitions will be described for simulations.

State-based formal methods [e.g. Event-B/RODIN (Abrial in Modeling in Event-B—system and software engineering. Cambridge University Press, Cambridge, 2010; Abrial et al. in Int J Softw Tools Technol Transf (STTT) 12(6):447–466, 2010)] for critical system development and verification are now well established, with track records including tool support and industrial applications. The focus of proof-based verification, in particular, is on safety properties. Liveness properties, which guarantee eventual, or converging computations of some requirements, are less well dealt with. Inductive reasoning about liveness is not explicitly supported. Liveness proofs are often complex and expensive, requiring high-skill levels on the part of the verification engineer. Fairness-based temporal logic approaches have been proposed to address this, e.g. TLA Lamport (ACM Trans Program Lang Syst 16(3):872–923, 1994) and that of Manna and Pnueli (Temporal verification of reactive systems—safety. Springer, New York, 1995). We contribute to this technology need by proposing a fairness-based method integrating temporal and first-order logic, proof and tools for modelling and verification of safety and liveness properties. The method is based on an integration of Event-B and TLA. Building on our previous work (Mery and Poppleton in Integrated formal methods, 10th international conference, IFM 2013, Turku, Finland, pp 208–222, 2013. doi: 10.1007/978-3-642-38613-8_15 ), we present the method via three example population protocols Angluin et al. (Distrib Comput 18(4):235–253, 2006). These were proposed as a theoretical framework for computability reasoning about Wireless Sensor Network and Mobile Ad-Hoc Network algorithms. Our examples present typical liveness and convergence requirements. We prove convergence results for the examples by integrated modelling and proof with Event-B/RODIN and TLA. We exploit existing proof rules, define and apply three new proof rules; soundness proofs are also provided. During the process we observe certain repeating patterns in the proofs. These are easily identified and reused because of the explicit nature of the reasoning.

Functional programs are well suited for concurrent execution due to the Church-Rosser property. However, for many applications there is still need to explicitly specify process systems instead of relying on compilers. Coordination languages provide one viable solution to the problem of specifying concurrent process systems, since they do not interfere with the properties of the language used for the algorithmic specification of the processes. The coordination language K2 to be proposed in this paper is based on a variant of colored Petri nets. It primarily defines process systems with deterministic behavior, but also allows for controlled forms of non-determinism. Specifications based on Petri nets offer several advantages. An underlying net calculus facilitates formal analysis and verification of basic safety and liveness properties. Graphical representations clearly expose structural dependencies among system components. Our variant of colored Petri nets provides several forms of net abstractions which facilitate the systematic construction of complex systems from small subsystems by composition. Recursive specifications can be used to adapt the structure of a process system to actual problem sizes or to varying input parameters.KeywordsInput StreamOutput StreamLiveness PropertyRecursive ProcessHierarchical ProcessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we introduce a framework composed of a syntax and its compositional Petri net semantics, for the specification and verification of properties (like authentication) of security protocols. The protocol agents (e.g., an initiator, a responder, a server, a trusted third party, ...) are formalized as roles, each of them having a predefined behavior depending on their global and also local knowledge (including for instance public, private and shared keys), and may interact in a potentially hostile environment. The main characteristics of our framework, is that it makes explicit, structured and formal, the usually implicit information necessary to analyse the protocol, for instance the public and private contextof execution. The roles and the environment are expressed using SPL processes and compositionally translated into high-level Petri nets, while the context specifying the global and local knowledge of the participants in the protocol is used to generate the corresponding initial marking (with respect to the studied property). Finally, this representation is used to analyse the protocol properties, applying techniques of simulation and model-checking on Petri nets. The complete approach is illustrated on the case study of the Kao-Chow authentication protocol.

The intelligent transportation systems problems of adaptive cruise control and variable timing for traffic intersection signals are explored with emphasis on verification of safety properties.

This volume contains the proceedings of the Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) held at Columbia University in New York City from July 5 to July 8, 2016. LICS is an annual international forum on theoretical and practical topics in computer science that relate to logic. The first LICS symposium was held in 1986, and LICS 2016 marks the thirtieth anniversary of that event.

Using a Real-Time Framework to Verify the Properties of Grafcet

A Novel Stochastic Game Via the Quantitative μ-calculus

A specification and verification method is presented for preventing denial of service in absence of failures and of integrity violations. The notion of user agreements is introduced, and it is argued that lack of specifications for these agreements and for simultaneity conditions makes it impossible to demonstrate denial-of-service prevention, in spite of demonstrably fair service access. The use of this method is illustrated with an example and it is explained why current methods for specification and verification of safety and liveness properties of concurrent programs do not handle this problem. The proposed specification and verification method is meant to augment current methods for secure system design. >

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

We investigate the power of counting in Group Isomorphism. We first leverage the count-free variant of the Weisfeiler–Leman Version I algorithm for groups [J. Brachter and P. Schweitzer, On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786] in tandem with bounded non-determinism and limited counting to improve the parallel complexity of isomorphism testing for several families of groups. These families include: • Direct products of non-Abelian simple groups. • Coprime extensions, where the normal Hall subgroup is Abelian and the complement is an [Formula: see text]-generated solvable group with solvability class [Formula: see text]. This notably includes instances where the complement is an [Formula: see text]-generated nilpotent group. This problem was previously known to be in [Formula: see text] [Y. Qiao, J. M. N. Sarma and B. Tang, On isomorphism testing of groups with normal Hall subgroups, in Proc. 28th Symp. Theoretical Aspects of Computer Science, Dagstuhl Castle, Leibniz Center for Informatics, 2011), pp. 567–578, doi:10.4230/LIPIcs. STACS.2011.567], and the complexity was recently improved to [Formula: see text] [J. A. Grochow and M. Levet, On the parallel complexity of group isomorphism via Weisfeiler–Leman, in 24th Int. Symp. Fundamentals of Computation Theory, eds. H. Fernau and K. Jansen, Lecture Notes in Computer Science, Vol. 14292, September 18–21, 2023, Trier, Germany (Springer, 2023), pp. 234–247]. • Graphical groups of class 2 and exponent [Formula: see text] [A. H. Mekler, Stability of nilpotent groups of class 2 and prime exponent, J. Symb. Logic 46(4) (1981) 781–788] arising from the CFI and twisted CFI graphs [J.-Y. Cai, M. Fürer and N. Immerman, An optimal lower bound on the number of variables for graph identification, Combinatorica 12(4) (1992) 389–410], respectively. In particular, our work improves upon previous results of Brachter and Schweitzer [On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786]. Notably, each of these families was previously known to be identified by the counting variant of the more powerful Weisfeiler–Leman Version II algorithm. We finally show that the q-ary count-free pebble game is unable to even distinguish Abelian groups. This extends the result of Grochow and Levet (ibid), who established the result in the case of [Formula: see text]. The general theme is that some counting appears necessary to place [Formula: see text] into [Formula: see text].

The correspondence between partial metrics and semivaluations

Reconfigurable systems have received much attention from academia and industry because they are efficient, agile, and reasonably priced, and they are the trend of all future systems. The chapter focuses on dynamic automatic reconfigurations of Control Systems to be classically modeled by Petri nets. Several modeling and verification methods for such systems are shown and compared before the introduction of the research work on feasible dynamic reconfigurations and the implementation of manufacturing systems based on Petri nets. Three different reconfiguration scenarios can be applied at run-time to such systems: Addition/Removal of places, Addition/Removal/Update of transitions, or finally, the simple modification of the initial marking. Three formal modules are defined accordingly, which allow the reconfigurations of the system’s Petri nets model: the first module to dynamically change places of the model, the second to dynamically reconfigure transitions within a given subset of places, and the third to modify the initial markings of places. To check the correct behavior of this architecture according to user requirements, the model checker SESA is applied for the verification of CTL-based properties of the proposed modules and also of the system. The contribution is applied to a real-world Benchmark Production System.

It is our pleasure to present the proceedings volume of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2018), held from9th to 12th July 2018 at Oxford (UK) as part of the Federated Logic Conference (FLoC 2018).

Handbook of logic in artificial intelligence and logic programming, Volume 3, Nonmonotonic reasoning and uncertain reasoning, edited by Dov M. Gabbay, C. J. Hogger, and J. A. Robinson, with D. Nute, Handbooks of logic in computer science and artificial intelligence and logic programming, Clarendon Press, Oxford University Press, Oxford, New York, etc., 1994, xix + 529 pp.– - Volume 6 Issue 4