Deriving a module of a multi agent system via Finite State Machine equation solving

In multiagent systems, there is a problem of constructing an agent that can work in different contexts satisfying different specifications. One of ways is to solve a system of corresponding automata equations. Since in general, the complexity of solving such equations is exponential w.r.t. to the number of states of the context and specification, the question arises whether a system of equations can be reduced to a single equation. In this paper, we consider two special cases when a system of equations under the parallel composition over Finite State Machines can be reduced to a single equation. For each case, it is shown how a corresponding single equation can be derived

The quotient in preorder theories

Seeking the largest solution to an expression of the form Ax 64 B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients

The Quotient in Preorder Theories

Seeking the largest solution to an expression of the form A x <= B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients.Comment: In Proceedings GandALF 2020, arXiv:2009.0936

Using Logic to Solve the Submodule Construction Problem

Abstract: Submodule construction is the problem of finding a new submodule which, together with a given submodule, provides a behavior that conforms to a given desired global behavior. A new formulation of this problem and its solution in first-order logic is presented, and it is shown how the known solutions to this problem in the context of various communication paradigms and specification formalisms can be derived. Communication paradigms are: synchronous rendezvous at several interfaces; interleaved rendezvous; input/output automata with complete or partial behavior specifications and with synchronous or interleaved communication. A new algorithm for deriving a progressive solution is also presented