Dense-choice Counter Machines revisited

This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines, and we provide new undecidability and decidability results. Using the first-order additive mixed theory of reals and integers, we give a logical characterization of the sets of configurations reachable by reversal-bounded Dense-choice Counter Machines

When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

An Effective Fixpoint Semantics for Linear Logic Programs

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of Tp working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming. Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete for an interesting class of LO programs encoding Petri Nets.Comment: 39 pages, 5 figures. To appear in Theory and Practice of Logic Programmin

On detectability of labeled Petri nets and finite automata

Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate detectability. This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong detectability. The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong detectability is strictly stronger than eventual strong detectability for labeled Petri nets and even for deterministic finite automata

Symbolic planning for heterogeneous robots through composition of their motion description languages

This dissertation introduces a new formalism to define compositions of interacting heterogeneous systems, described by extended motion description languages (MDLes). The properties of the composition system are analyzed and an automatic process to generate sequential atom plan is introduced. The novelty of the formalism is in producing a composed system with a behavior that could be a superset of the union of the behaviors of its generators. As robotic systems perform increasingly complex tasks, people resort increasingly to switching or hybrid control algorithms. A need arises for a formalism to compose different robotic behaviors and meet a final target. The significant work produced to date on various aspects of robotics arguably has not yet effectively captured the interaction between systems. Another problem in motion control is automating the process of planning and it has been recognized that there is a gap between high level planning algorithms and low level motion control implementation. This dissertation is an attempt to address these problems. A new composition system is given and the properties are checked. We allow systems to have additional cooperative transitions and become active only when the systems are composed with other systems appropriately. We distinguish between events associated with transitions a push-down automaton representing an MDLe can take autonomously, and events that cannot initiate transitions. Among the latter, there can be events that when synchronized with some of another push-down automaton, become active and do initiate transitions. We identify MDLes as recursive systems in some basic process algebra (BPA) written in Greibach Normal Form. By identifying MDLes as a subclass of BPAs, we are able to borrow the syntax and semantics of the BPAs merge operator (instead of defining a new MDLe operator), and thus establish closeness and decidability properties for MDLe compositions. We introduce an instance of the sliding block puzzle as a multi-robot hybrid system. We automate the process of planning and dictate how the behaviors are sequentially synthesized into plans that drive the system into a desired state. The decidability result gives us hope to abstract the system to the point that some of the available model checkers can be used to construct motion plans. The new notion of system composition allows us to capture the interaction between systems and we realize that the whole system can do more than the sum of its parts. The framework can be used on groups of heterogeneous robotic systems to communicate and allocate tasks among themselves, and sort through possible solutions to find a plan of action without human intervention or guidance

Discrete Semantics for Hybrid Automata

Many natural systems exhibit a hybrid behavior characterized by a set of continuous laws which are switched by discrete events. Such behaviors can be described in a very natural way by a class of automata called hybrid automata. Their evolution are represented by both dynamical systems on dense domains and discrete transitions. Once a real system is modeled in a such framework, one may want to analyze it by applying automatic techniques, such as Model Checking or Abstract Interpretation. Unfortunately, the discrete/continuous evolutions not only provide hybrid automata of great flexibility, but they are also at the root of many undecidability phenomena. This paper addresses issues regarding the decidability of the reachability problem for hybrid automata (i.e., "can the system reach a state a from a state b?") by proposing an "inaccurate" semantics. In particular, after observing that dense sets are often abstractions of real world domains, we suggest, especially in the context of biological simulation, to avoid the ability of distinguishing between values whose distance is less than a fixed \u3b5. On the ground of the above considerations, we propose a new semantics for first-order formul\ue6 which guarantees the decidability of reachability. We conclude providing a paradigmatic biological example showing that the new semantics mimics the real world behavior better than the precise one

Place-Boundedness for Vector Addition Systems with one zero-test

Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer cover, hybrid between the reachability and cover sets, reclaiming accuracy on one component. We show that this filtered cover is still recursive, but that equality of two such filtered covers, even for usual Vector Addition Systems (with no zero-test), is undecidable