Three variations of observation equivalence preserving synthesis abstraction

In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor

A novel EGs-based framework for systematic propositional-formula simplification

Funding: Bowles is partially supported by Austrian FWF Meitner Fellowship M-3338 N.This paper presents a novel simplification calculus for propositional logic derived from Peirce’s Existential Graphs’ rules of inference and implication graphs. Our rules can be applied to arbitrary propositional logic formulae (not only in CNF), are equivalence-preserving, guarantee a monotonically decreasing number of clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. We further show how this rule can be extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures. Finally, we discuss the complexity and implementation of our framework as a solver-agnostic algorithm to simplify Boolean satisfiability problems and arbitrary propositional formula.Postprin

Congruences in ordered sets and LU compatible equivalences

summary:A concept of equivalence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence

Equivalence-preserving first-order unfold/fold transformation systems

AbstractTwo unfold/fold transformation systems for first-order programs, one basic and the other extended, are presented. The systems comprise an unfolding rule, a folding rule and a replacement rule. They are intended to work with a first-order theory Δ specifying the meaning of primitives, on top of which new relations are built by programs. They preserve the provability relationship Δ ∪ Γ ⊬ G between a call-consistent program Γ and a goal formula G such that Γ is strict with respect to G. They also preserve the logical consequence relationship in three-valued logic

An algorithm for compositional nonblocking verification of extended finite-state machines

This paper describes an approach for compositional nonblocking verification of discrete event systems modelled as extended finite-state machines (EFSM). Previous results about finite-state machines in lock-step synchronisation are generalised and applied to EFSMs communicating via shared variables. This gives rise to an EFSM-based conflict check algorithm that composes EFSMs gradually and partially unfolds variables as needed. At each step, components are simplified using conflict-equivalence preserving abstraction. The algorithm has been implemented in the discrete event systems tool Supremica. The paper presents experimental results for the verification of two scalable manufacturing system models, and shows that the EFSM-based algorithm verifies some large models faster than previously used methods