Complexity of Decision Problems for Mixed and Modal Specifications

Antonik, Adam; Huth, Michael; Larsen, Kim Guldstrand; Nyman, Ulrik; Wąsowski, Andrzej

doi:10.1007/978-3-540-78499-9_9

Cited by 21 publications

(37 citation statements)

References 16 publications

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“…Consider DMTSs F and G from Figure 2. The two models are consistent, with the maximal consistency relation C = {(0, 5), (3,5), (4,6), (0, 7), (1,8), (2,8)}. DMTS H is their merge.…”

Section: Definition 13 (Observational Dmtss Consistency Relation (Basmentioning

confidence: 99%

Observational Refinement and Merge for Disjunctive MTSs

Ben-David

Chećhik

Uchitel

2016

Automated Technology for Verification and Analysis

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Abstract. Modal Transition System (MTS) is a well studied formalism for partial model specification. It allows a modeller to distinguish between required, prohibited and possible transitions. Disjunctive MTS (DMTS) is an extension of MTS that has been getting attention in recent years. A key concept for (D)MTS is refinement, supporting a development process where abstract specifications are gradually refined into more concrete ones. Refinement comes in different flavours: strong, observational (where τ -labelled transitions are taken into account), and alphabet (allowing the comparison of models defined on different alphabets). Another important operation on (D)MTS is that of merge: given two models M and N , their merge is a model P which refines both M and N , and which is the least refined one. In this paper, we fill several missing parts in the theory of DMTS refinement and merge. First and foremost, we define observational refinement for DMTS. While an elementary concept, such a definition is missing from the literature to the best of our knowledge. We prove that our definition is sound and that it complies with all relevant definitions from the literature. Based on the new observational refinement for DMTS, we examine the question of DMTS merge, which was defined so far for strong refinement only. We show that observational merge can be achieved as a natural extension of the existing algorithm for strong merge of DMTS. For alphabet merge however, the situation is different. We prove that DMTSs do not have a merge under alphabet refinement.

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“…Consider DMTSs F and G from Figure 2. The two models are consistent, with the maximal consistency relation C = {(0, 5), (3,5), (4,6), (0, 7), (1,8), (2,8)}. DMTS H is their merge.…”

Section: Definition 13 (Observational Dmtss Consistency Relation (Basmentioning

confidence: 99%

Observational Refinement and Merge for Disjunctive MTSs

Ben-David

Chećhik

Uchitel

2016

Automated Technology for Verification and Analysis

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“…In [1,16,17,19,25,33], (variants of) MTSs have been proposed for modelling and verifying the behaviour of product families. We have extended MTSs in [17] to allow modelling different notions of behavioural variability.…”

Section: Related Workmentioning

confidence: 99%

“…To overcome the limitation pointed out earlier of using LTSs as modelling framework for product families, Modal Transition Systems (MTSs) [26] and several variants have been proposed to capture variability in product family specifications [1,16,17,19,25,33]. In an MTS, transitions are either possible (may) or required (must ), corresponding to the notion of optional or mandatory features in product families.…”

Section: Modal Transition Systemsmentioning

confidence: 99%

“…Many years after their introduction in [26], Modal Transition Systems (MTSs) and several variants have been proposed as a formal model for defining product families [1,16,17,19,25,33]. An MTS is a Labelled Transition System (LTS) with a distinction among so-called may and must transitions, which can be seen as optional or mandatory for the products of the family.…”

Section: Introductionmentioning

confidence: 99%

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A Logical Framework to Deal with Variability

Asirelli

Beek

Gnesi

2010

Lecture Notes in Computer Science

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Abstract. We present a logical framework that is able to deal with variability in product family descriptions. The temporal logic MHML is based on the classical Hennessy-Milner logic with Until and we interpret it over Modal Transition Systems (MTSs). MTSs extend the classical notion of Labelled Transition Systems by distinguishing possible (may) and required (must) transitions: these two types of transitions are useful to describe variability in behavioural descriptions of product families. This leads to a novel deontic interpretation of the classical modal and temporal operators, which allows the expression of both constraints over the products of a family and constraints over their behaviour in a single logical framework. Finally, we sketch model-checking algorithms to verify MHML formulae as well as a way to derive correct products from a product family description.

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“…While for a number of other problems, like the common implementation problem, a matching complexity lower and upper bounds were given [2,14,3], the question of the exact complexity of thorough refinement checking between two finite MTSs remained unanswered.…”

Section: Introductionmentioning

confidence: 99%

Checking Thorough Refinement on Modal Transition Systems Is EXPTIME-Complete

Beneš

Křetínský

Larsen

et al. 2009

Theoretical Aspects of Computing - ICTAC 2009

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Modal transition systems (MTS), a specification formalism introduced more than 20 years ago, has recently received a considerable attention in several different areas. 1 or has a fixed size, the running time of the algorithm becomes polynomial. The lower-bound proof is achieved by reduction from the acceptance problem of alternating linear bounded automata and the problem remains EXPTIME-hard even if the left-hand side MTS is fixed.

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Complexity of Decision Problems for Mixed and Modal Specifications

Cited by 21 publications

References 16 publications

Observational Refinement and Merge for Disjunctive MTSs

Observational Refinement and Merge for Disjunctive MTSs

A Logical Framework to Deal with Variability

Checking Thorough Refinement on Modal Transition Systems Is EXPTIME-Complete

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