In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical isotopy invariants: augmentation category, unital $A_{\infty}$-category, which lifts set of augmentations Chekanov-Eliashberg DGA, DG category constructible sheaves on front plane, with micro-support at contact infinity controlled by graph. other words, generalizing [21], prov...

An automaton with concurrency relations A is a labeled transition system with a collection of binary relations indicating when two actions in a given state of the automaton can occur independently of each other. The concurrency relations induce a natural equivalence relation for nite computation sequences. We investigate two graph-theoretic representations of the equivalence classes of computat...

We study linear complementarity problems depending on parameters in the right-hand side and (or) in the matrix. For the case that all elements of the right-hand side are independent parameters we give a new proof for the equivalence of three diierent important local properties of the corresponding solution set map in a neighbourhood of an element of its graph. For one-and multiparametric proble...

CCS can be considered as a most natural extension of finite state automata in which interaction is made possible thanks to parallel composition. We propose here a similar extension for top-down tree automata. We introduce a parallel composition which is parameterized by a graph at the vertices of which subprocesses are located. Communication is allowed only between subprocesses related by an ed...

This paper presents congruence results of a behavioural equivalence on a graph rewriting model of concurrent pro cesses with higher-order communication. A bipartite di rected acyclic graph represents a concurrent system that consists of a number of processes and messages in our model. The model presented here makes it possible to repre sent local names that their scopes are not nested. We show ...

The paper considers an equivalence relation in the set of vertices of a bipartite graph. Some numerical characteristics showing the cardinality of equivalence classes are introduced. A combinatorial identity that is in relationship to these characteristics of the set of all bipartite graphs of the type g = 〈Rg ∪Cg , Eg〉 is formulated and proved, where V = Rg ∪ Cg is the set of vertices, Eg is t...

Given a graph G we provide dynamic programming algorithms for many locally checkable vertex subset and vertex partitioning problems. Their runtime is polynomial in the number of equivalence classes of problem-specific equivalence relations on subsets of vertices, defined on a given decomposition tree of G. Using these algorithms all these problems become solvable in polynomial time for many wel...

Based on our existing works, this paper firstly gives clock region equivalence PVS specification, and then constructs the reachable region graph for a given Timed Automaton (TA) via characterizing some kinds of clock regions, finally analyses the reachable states using the region graph. These works can conveniently analysis some real-time system in the form of TA model. A case study is investig...

concurrent semantics are also defined. Three classical observations for concurrent semantics — interleaving, partial ordering and mixed ordering — are defined on the graph derivations. Bisimulation is exploited to obtain three equivalences of π-calculus agents corresponding to the observations. As expected, the ordinary observational equivalence for the π-calculus is re-obtained in this context...

In this paper, we explore the structure of the set of all regular equivalences (White and Reitz 1983) proving that it forms a lattice, and suggest a general approach to computing certain elements of the lattice. The resulting algorithm represents a useful complement to the White and Reitz algorithm, which can only find the maximal regular equivalence of a graph. Using this algorithm, it is poss...