Network Invariants for Real-Time Systems

Software Engineering for Parallel and …, 1998

In this paper we define timed regular expressions to de-scribe the timed behaviour of parallel real-time systems and consider the problem of checking algorithmically the set of timed behaviours defined by timed regular expressions for a real-time requirement specified by a linear ...

Theoretical Computer Science, 2020

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2000

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called ρ, n -equivalence, where ρ is a set of actions and n is a natural number. It is proved that two transition systems are ρ, n -equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in ρ, and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set ρ of actions and a natural number n, produces a reduced transition system ρ, nequivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving ρ, n -equivalence.

Proceedings Eighth International Symposium on Temporal Representation and Reasoning. TIME 2001, 2000

We present a new real-time temporal logic for the specification and verification of discrete quantitative temporal properties. This logic is an extension of the well-known logic CTL. Its semantics is defined on discrete time transition systems which are in turn interpreted in an abstract manner instead of the usual stuttering interpretation. Hence, our approach directly supports abstractions of real-time systems by ignoring irrelevant qualitative properties, but without loosing any quantitative information. We analyse the complexity of the presented model checking algorithm and furthermore present a fragment of the logic that can be efficiently checked.

Logic in Computer Science, …, 1990

This research extends CTL model-checking to the analysis of real-time systems, whose correctness depends on the magnitudes of the timing delays. For specifications, the syntax of CTL is extended to allow quantitative temporal operators. The formulas of the resulting logic, TCTL, are interpretation over continuous computation trees, trees in which paths are maps from the set of nonnegative reals to system states. To model finite-state systems the notion of timed graphs is introduced-state-transition graphs extended with a ...

Lecture Notes in Computer Science, 2016

Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (e.g., winds). Moreover, goals are often specified using explicit time constraints which must be satisfied by the system perpetually. For example, drones carrying out the surveillance of some area must always have recent pictures, i.e., at most M time units old, of some strategic locations. This paper proposes a Multiset Rewriting language with explicit time for specifying and analysing TSDSes. We introduce two properties, realizability (some trace is good) and survivability (where, in addition, all admissible traces are good). A good trace is an infinite trace in which goals are perpetually satisfied. We propose a class of systems called progressive timed systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems both the realizability and the survivability problems are PSPACE-complete. Furthermore, if we impose a bound on time (as in bounded model-checking), we show that for PTS, realizability becomes NP-complete, while survivability is in the ∆ p 2 class of the polynomial hierarchy. Finally, we demonstrate that the rewriting logic system Maude can be used to automate time bounded verification of PTS.

2017

Given a logical formula and a system described as the composition of arbitrarily many copies of some process template, the parameterized model checking problem wants to establish whether the system satisfies the formula. The focus is on the fact that the property should not depend on the actual number of participating processes. Exactly this, makes the problem equivalent to verifying an infinite state system, and thus undecidable problem in general. Several authors identified relevant sub-classes of systems or formulae to be model checked. In this work we study the parameterized model checking problem of real-time systems against real-time temporal logics. In particular we study the possibility of finding an upper bound to the size of the system, known as cutoff, ensuring that adding more participants does not change the set of satisfiable formulae. A distinction exists between dynamic cutoffs, depending both on the process templates and the formula, and static cutoffs, that only co...

2009 International Conference on Embedded Software and Systems, 2009

Formal methods play an important role in the development of safety-critical systems. Their well-defined semantics can be employed for automatic formal system verification. Modelchecking, a well-established formal verification technique, is however often restricted to an abstract level due to complexity reasons. For example, checking temporal system behaviour with respect to hardware architectures and operating systems is often not possible. Real-time scheduling theory on the other hand provides efficient techniques for temporal analysis of real-world systems at architecture level. However, models used in real-time scheduling theory usually lack a semantics that is compatible to those used by formal specifications. This prevents to verify temporal system behaviour at the architecture level with the same formal methods. We present an approach that combines a timed automata representation of task networks and efficient scheduling analysis techniques. Based on existing task network formalisms we define a consistent timed automaton model, and a mapping between both formalisms. We prove that the mapping induces behavioural equivalence of the models. We show an application of the approach by verifying task networks against Live Sequence Charts (LSC).

2014

Quasi-equal clock reduction for networks of timed automata replaces equivalence classes of clocks which are equal except for unstable phases, i.e., points in time where these clocks differ on their valuation, by a single representative clock. An existing approach yields significant reductions of the overall verification time but is limited to so-called wellformed networks and local queries, i.e., queries which refer to a single timed automaton only. In this work we present two new transformations. The first, for networks of timed automata, summarises unstable phases without losing information under weaker well-formedness assumptions than needed by the existing approach. The second, for queries, now supports the full query language of Uppaal. We demonstrate that the cost of verifying non-local properties is much lower in transformed networks than in their original counterparts with quasi-equal clocks.

Lecture Notes in Computer Science, 2021

This paper develops a Multiset Rewriting language with explicit time for the specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals are often specified using explicit time constraints. A good trace is an infinite trace in which the goals are satisfied perpetually despite possible interference from the environment. In our previous work [16], we discussed two desirable properties of TSDSes, realizability (there exists a good trace) and survivability (where, in addition, all admissible traces are good). Here we consider two additional properties, recoverability (all compliant traces do not reach points-of-no-return) and reliability (the system can always continue functioning using a good trace). Following [16], we focus on a class of systems called Progressing Timed Systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems the properties of recoverability and reliability coincide and are PSPACE-complete. Moreover, if we impose a bound on time (as in bounded model-checking), we show that for PTS the reliability property is in the Π p 2 class of the polynomial hierarchy, a subclass of PSPACE. We also show that the bounded survivability is both NP-hard and coNP-hard.

IEEE Transactions on Software Engineering, 1994

The problem of formally analyzing properties of real-time systems is addressed. A method is proposed that allows specifying system properties in the TRIO language (an extension of temporal logic suitable to deal explicitly with the "time" variable and to measure it) and modeling the system as a timed Petri net. It is argued that such an approach is more general than analyzing program properties. The proof method is based on an axiomatization of timed Petri nets in terms of TRIO so that their properties can be derived as suitable theorems in much the same spirit as classical Hoare's method allows proving properties of programs coded in a Pascal-like language. The method is then exemplified through two classical "benchmarks" of the literature on concurrent and real-time systems, namely an elevator system and the dining philosophers problem. A thorough review of the related literature and a comparison thereof with the new method is also provided. Possible alternative methods, theoretical extensions, and practical applications are briefly discussed.

Formal Aspects of Computing, 2009

Following the trend to combine techniques to cover several facets of the development of modern systems, an integration of Z and CSP, called Circus , has been proposed as a refinement language; its relational model, based on the unifying theories of programming (UTP), justifies refinement in the context of both Z and CSP. In this paper, we introduce Circus Time , a timed extension of Circus , and present a new UTP time theory, which we use to give semantics to Circus Time and to validate some of its laws. In addition, we provide a framework for validation of timed programs based on FDR, the CSP model-checker. In this technique, a syntactic transformation strategy is used to split a timed program into two parallel components: an untimed program that uses timer events, and a collection of timers. We show that, with the timer events, it is possible to reason about time properties in the untimed language, and so, using FDR. Soundness is established using a Galois connection between the u...

Proceedings of the 31st annual conference on Design automation conference - DAC '94, 1994

An important practical approach to automatic verification of finite state concurrent systems is temporal logic model checking. However, a major barrier towards wider application of such methods is the state explosion problem that often occurs during the composition of complex communicating systems. In addition to being large, many systems have very deep state spaces as well.

Electronic Notes in Theoretical Computer Science, 2006

We propose a format of predicate diagrams for the verification of real-time systems. We consider systems that are defined as extended timed graphs, a format that combines timed automata and constructs for modeling data, possibly over infinite domains. Predicate diagrams are succinct and intuitive representations of Boolean abstractions. They also represent an interface between deductive tools used to establish the correctness of an abstraction, and model checking tools that can verify behavioral properties of finite-state models. The contribution of this paper is to extend the format of predicate diagrams to timed systems. We also establish a set of verification conditions that are sufficient to prove that a given predicate diagram is a correct abstraction of an extended timed graph. The formalism is supported by a toolkit, and we demonstrate its use at the hand of Fischer's real-time mutualexclusion protocol.

DAIMI Report Series, 1993

This thesis is concerned with the verification of concurrent systems modelled by process algebras. It provides methods and techniques for reasoning about temporal properties as described by assertions from an expressive modal logic -- the modal µ-calculus. It describes a compositional approach to model checking, efficient local and global algorithms for model checking finite-state systems, a general local fixed-point finding algorithm, a proof system for model checking infinite-state systems, a categorical completeness result for an intuitionistic version of the modal µ-calculus, and finally it shows some novel applications of the logic for expressing behavioural relations.