Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic, such as LTL and the like. These logics are “point-wise” interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those constraining the temporal relations between pairs of temporally extended events or involving temporal aggregations, which are inherently “interval-based”, and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham’s interval temporal logic HS over finite Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against finite Kripke structures is decidable by a suitable small model theorem, and we provide a lower bound to its computational complexity
Motivation: Identification of differential expressed genes has led to countless new discoveries. However, differentially expressed genes are only a proxy for finding dysregulated pathways. The problem is to identify how the network of regulatory and physical interactions rewires in different conditions or in disease.Results: We developed a procedure named DINA (DIfferential Network Analysis), which is able to identify set of genes, whose co-regulation is condition-specific, starting from a collection of condition-specific gene expression profiles. DINA is also able to predict which transcription factors (TFs) may be responsible for the pathway condition-specific co-regulation. We derived 30 tissue-specific gene networks in human and identified several metabolic pathways as the most differentially regulated across the tissues. We correctly identified TFs such as Nuclear Receptors as their main regulators and demonstrated that a gene with unknown function (YEATS2) acts as a negative regulator of hepatocyte metabolism. Finally, we showed that DINA can be used to make hypotheses on dysregulated pathways during disease progression. By analyzing gene expression profiles across primary and transformed hepatocytes, DINA identified hepatocarcinoma-specific metabolic and transcriptional pathway dysregulation.Availability: We implemented an on-line web-tool http://dina.tigem.it enabling the user to apply DINA to identify tissue-specific pathways or gene signatures.Contact: dibernardo@tigem.itSupplementary information: Supplementary data are available at Bioinformatics online.
We present a new semantics of Statecharts that excludes failures and a compositional formulation of this semantics based on Labelled Transition Systems (LTS). We consider a hierarchy of LTS equivalences and we study their congruence properties w.r. to statechart operators
Model checking allows one to automatically verify a specification of the expected properties of a system against a formal model of its behaviour (generally, a Kripke structure). Point-based temporal logics, such as LTL, CTL, and CTL * , that describe how the system evolves state-by-state, are commonly used as specification languages. They proved themselves quite successful in a variety of application domains. However, properties constraining the temporal ordering of temporally extended events as well as properties involving temporal aggregations, which are inherently intervalbased, can not be properly dealt with by them. Interval temporal logics (ITLs), that take intervals as their primitive temporal entities, turn out to be well-suited for the specification and verification of interval properties of computations (we interpret all the tracks of a Kripke structure as computation intervals).In this paper, we study the model checking problem for some fragments of Halpern and Shoham's modal logic of time intervals (HS). HS features one modality for each possible ordering relation between pairs of intervals (the so-called Allen's relations). First, we describe an EXPSPACE model checking algorithm for the HS fragment of Allen's relations meets, met-by, starts, started-by, and finishes, which exploits the possibility of finding, for each track (of unbounded length), an equivalent bounded-length track representative. While checking a property, it only needs to consider tracks whose length does not exceed the given bound. Then, we prove the model checking problem for such a fragment to be PSPACE-hard. Finally, we identify other well-behaved HS fragments which are expressive enough to capture meaningful interval properties of systems, such as mutual exclusion, state reachability, and non-starvation, and whose computational complexity is less than or equal to that of LTL.Keywords: Model checking, interval temporal logics, computational complexity 2010 MSC: 03B70, 68Q60 ✩ This paper is an extended and revised version of [22] and [21].
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