128 research outputs found
Fixpoint Games on Continuous Lattices
Many analysis and verifications tasks, such as static program analyses and
model-checking for temporal logics reduce to the solution of systems of
equations over suitable lattices. Inspired by recent work on lattice-theoretic
progress measures, we develop a game-theoretical approach to the solution of
systems of monotone equations over lattices, where for each single equation
either the least or greatest solution is taken. A simple parity game, referred
to as fixpoint game, is defined that provides a correct and complete
characterisation of the solution of equation systems over continuous lattices,
a quite general class of lattices widely used in semantics. For powerset
lattices the fixpoint game is intimately connected with classical parity games
for -calculus model-checking, whose solution can exploit as a key tool
Jurdzi\'nski's small progress measures. We show how the notion of progress
measure can be naturally generalised to fixpoint games over continuous lattices
and we prove the existence of small progress measures. Our results lead to a
constructive formulation of progress measures as (least) fixpoints. We refine
this characterisation by introducing the notion of selection that allows one to
constrain the plays in the parity game, enabling an effective (and possibly
efficient) solution of the game, and thus of the associated verification
problem. We also propose a logic for specifying the moves of the existential
player that can be used to systematically derive simplified equations for
efficiently computing progress measures. We discuss potential applications to
the model-checking of latticed -calculi and to the solution of fixpoint
equations systems over the reals
Conditional Transition Systems with Upgrades
We introduce a variant of transition systems, where activation of transitions
depends on conditions of the environment and upgrades during runtime
potentially create additional transitions. Using a cornerstone result in
lattice theory, we show that such transition systems can be modelled in two
ways: as conditional transition systems (CTS) with a partial order on
conditions, or as lattice transition systems (LaTS), where transitions are
labelled with the elements from a distributive lattice. We define equivalent
notions of bisimilarity for both variants and characterise them via a
bisimulation game.
We explain how conditional transition systems are related to featured
transition systems for the modelling of software product lines. Furthermore, we
show how to compute bisimilarity symbolically via BDDs by defining an operation
on BDDs that approximates an element of a Boolean algebra into a lattice. We
have implemented our procedure and provide runtime results
Bisimulations for Fuzzy Transition Systems revisited
Bisimulation is a well-known behavioral equivalence for discrete event systems and has recently been adopted and developed in fuzzy systems. In this paper, we propose a new bisimulation, i.e., the group-by-group fuzzy bisimulation, for fuzzy transition systems. It relaxes the fully matching requirement of the bisimulation definition proposed by Cao et al. and can equate more pairs of states which are deemed to be equivalent
intuitively, but which cannot be equated in previous definitions. We carry out a systematic investigation on this new notion of bisimulation. In particular, a fixed point characterization of the group-by-group fuzzy bisimilarity is given, based on which, we provide a polynomial-time algorithm to check whether two states
in a fuzzy transition system are group-by-group fuzzy bisimilar. Moreover, a modal logic, which is an extension of the Hennessy-Milner logic, is presented to completely characterize the group-by-group fuzzy bisimilarity
A Framework for Compositional Verification of Multi-valued Systems via Abstraction-Refinement
We present a framework for fully automated compositional verification of µ-calculus specifications over multi-valued systems, based on multivalued abstraction and refinement. Multi-valued models are widely used in many applications of model checking. They enable a more precise modeling of systems by distinguishing several levels of uncertainty and inconsistency. Successful verification tools such as STE (for hardware) and YASM (for software) are based on multi-valued models. Our compositional approach model checks individual components of a system. Only if all individual checks return indefinite values, the parts of the components which are responsible for these values, are composed and checked. Thus the construction of the full system is avoided. If the latter check is still indefinite, then a refinement is needed. We formalize our framework based on bilattices, consisting of a truth lattice and an information lattice. Formulas interpreted over a multi-valued model are evaluated w.r.t. to the truth lattice. On the other hand, refinement is now aimed at increasing the information level of model details, thus also increasing the information level of the model checking result. Based on the two lattices, we suggest how multi-valued models should be composed, checked, and refined
Tools and Algorithms for the Construction and Analysis of Systems
This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers
A coalgebraic treatment of conditional transition systems with upgrades
We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these coalgebras live: Kleisli categories based on the reader and on the so-called lattice monad over Poset. We study two different functors describing the branching type of the coalgebra and investigate the resulting behavioural equivalence. Furthermore we show how an existing algorithm for coalgebra minimisation can be instantiated to derive behavioural equivalences in this setting
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