Monotonic Abstraction Techniques: from Parametric to Software Model Checking

Abstract

Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting in previous papers of ours and applied to the verification of fault tolerant systems under the so-called 'stopping failures' model. The declarative reinterpretation consists in logical techniques (quantifier relativizations and, especially, quantifier instantiations) making sense in a broader context. In fact, we recently showed that such techniques can over-approximate array accelerations, so that they can be employed as a meaningful (and practically effective) component of CEGAR loops in software model checking too. 1 c 1 to c 2 . More precisely, the abstraction kills (deletes) all the processes inside the configuration which violate the universal condition. Since the abstract transition relation is an over-approximation of the original one, proving a safety property in the abstract system implies that the property also holds in the original system." Array-Based SystemsArray-based systems were first introduced in [34]: the underlying idea is that of specifying systems of various nature using array theories like those studied in [24,25] and implemented in common SMTsolvers. Array theories are multi-sorted and very flexible; typically one has three sorts: for indexes, elements and arrays. To specify a distributed system, one can use the index sort to model processes and

Formal Modeling and SMT-Based Parameterized Verification of Data-Aware BPMN

“…Universal guards in tran-sition formulae could be very useful in specifications: for example, they would allow us to specify a branch in a job hiring process that is followed only if no applicant satisfies a certain condition. The question has been debated since longtime in the literature and the most effective solution so far is the introduction of suitable "monotonic abstractions" (see [1] for a survey). Notably, this is already implemented in MCMT.…”

“…We focus here on private, single-pool processes, analyzed considering a single case, similarly to soudness analysis in workflow nets [29]. 1 Incoming messages are therefore handled as pure nondeterministic events. The model combines a wide range of (blockstructured) BPMN control-flow constructs with task, event-reaction, and condition logic that inspect and modify persistent as well as case data.…”

“…Application(Jcid:JobcatID,Uid:UserID, Eligible:Bool) NumScore is a finite-domain type containing 100 scores in the range [1,100]. For readability, we use the usual comparison predicates for variables of type NumScore: this is syntactic sugar and does not require to introduce datatype predicates in our framework.…”

“…Consistently with the BPMN standard, we consider two main forms of data: case data 1 , instantiated and manipulated on a per-case basis; persistent data (cf. data store references in BPMN), accounting for global data that are accessed by all cases.…”

“…To manage key information about the applications submitted for the various job hirings, including data on users, the score they receive after having been interviewed and their eligibility, the company employs the repository D.repo that consists of one relation schema Application (Jid:jobId, Jcid:jobcatID, U id:userID, N ame:StringName, Age:NumAge, Score:NumScore, Eligible:Bool) Notice that NumScore is a finite-domain type containing 100 values in the range [1,100], and it is used to assign an overall score to each candidate application. For readability, we use the usual predicates <, >, and = to compare variables of type NumScore: this is syntactic sugar and does not require to introduce rigid predicates in our framework.…”