2020 # Structural Invariants for the Verification of Systems with Parameterized Architectures

**Abstract:** We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g. rendez-vous, broadcast) and the topology of the system (e.g. pipeline, ring). The logic can be easily embedded in monadic second order logic of κ ≥ 1 successor…

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(40 citation statements)

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“…Concerning trees, the tree-dfs example models a binary tree architecture traversed by a token in depth-first order, while tree-back-root and tree-linked-leaves(-generic) go beyond trees, modeling hierarchical systems with parent-children communication on top of which the nodes communicate with the root and the leaves are linked in a token-ring, respectively. These examples could not have been described using first order logic, as in [4]. The verification problems considered could be solved in less than 1 second, with the exception of the critical section violations for the tree-linked-leaves(-generic) examples, that require mutex, in addition to trap invariants.…”

confidence: 99%

“…Concerning trees, the tree-dfs example models a binary tree architecture traversed by a token in depth-first order, while tree-back-root and tree-linked-leaves(-generic) go beyond trees, modeling hierarchical systems with parent-children communication on top of which the nodes communicate with the root and the leaves are linked in a token-ring, respectively. These examples could not have been described using first order logic, as in [4]. The verification problems considered could be solved in less than 1 second, with the exception of the critical section violations for the tree-linked-leaves(-generic) examples, that require mutex, in addition to trap invariants.…”

confidence: 99%

“…As demonstrated in Section 3 the pre-and postset of transitions, as well as general sets of places in a PN describing the execution semantics can be defined in WSκS. Hence, we present the definitions of the following formulae only in the full version of this article [16] and just give the intuitions here.…”

confidence: 99%

“…MIL was used for the description of parametric rendezvous and broadcast communication and applied for developing an automated method for detecting deadlocks. In the same line, in [11], an Interaction Logic with One Successor (IL1S) was developed for describing rendezvous and broadcast communications, and the architectures of parametric systems. IL1S was proved to be decidable and used for checking correctness of safety properties of parametric systems.…”

confidence: 99%

“…The interface of an LTS corresponds to its set of labels, called ports. Then, communications of components are defined by interactions, i.e., sets of ports, that can be represented by formulas of propositional interaction logic (PIL for short) [10,11,28]. Hence, firstly we need to recall PIL.…”

confidence: 99%