This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short). The technique is based on the concept of bounded satisfiability, and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of quantifierfree equality and uninterpreted functions combined with D. Similarly to standard LTL, where bounded model-checking and SAT-solvers can be used as an alternative to automata-theoretic approaches to model-checking, our approach allows users to solve the satisfiability problem for CLTLB(D) formulae through SMT-solving techniques, rather than by checking the emptiness of the language of a suitable automaton. The technique is effective, and it has been implemented in our Zot formal verification tool.

This paper defines CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. The paper introduces suitable restrictions and assumptions that make the satisfiability problem decidable in many cases, although the problem is undecidable in the general case. Decidability is shown for a large class of constraint systems, and an encoding into Boolean logic is defined. This paves the way for applying existing SMT-solvers for checking the Bounded Reachability problem, as shown by various experimental results

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An important problem that arises during the execution of service-based applications concerns the ability to determine whether a running service can be substituted with one with a different interface, for example if the former is no longer available. Standard Bounded Model Checking techniques can be used to perform this check, but they must be able to provide answers very quickly, lest the check hampers the operativeness of the application, instead of aiding it. The problem becomes even more complex when conversational services are considered, i.e., services that expose operations that have Input/Output data dependencies among them. In this paper we introduce a formal verification technique for an extension of Linear Temporal Logic that allows users to include in formulae constraints on integer variables. This technique applied to the substitutability problem for conversational services is shown to be considerably faster and with smaller memory footprint than existing ones.

In the past years, the adoption of adaptive systems has increased in many fields of computer science, such as databases and software engineering. These systems are able to automatically react to events by collecting information from the external environment and generating new events. However, the collection of data is often hampered by uncertainty and vagueness. The decision-making mechanism used to produce a reaction is also imprecise and cannot be evaluated in a crisp way, as it depends on vague temporal constraints expressed by humans. Logic has been extensively used as an abstraction to express vagueness in the satisfaction of system properties, as well as to enrich existing modeling formalisms. However, existing attempts to fuzzify the temporal modalities still have some limitations. Existing fuzzy temporal languages are generally obtained from classical temporal logic by replacing classical connectives or propositions with their fuzzy counterparts. Hence, these languages do not allow us to represent temporal properties, such as "almost always" and "soon," in which the notion of time is inherently fuzzy. To overcome these limitations, we propose a temporal framework, fuzzy-time temporal logic (FTL), to express vagueness on time. This framework formally defines a set of fuzzy temporal modalities that can be customized by choosing a specific semantics for the connectives. The semantics of the language is sound, and the introduced modalities respect a set of mutual relations. We also prove that under the assumption that all events are crisp, FTL reduces to linear temporal logic (LTL). Moreover, for some of the possible fuzzy interpretations of the connectives, we identify adequate sets of temporal operators, from which it is possible to derive all of the other ones.