We give a deterministic algorithm to construct a graph with no loops (a tree or a forest) whose vertices are the points of a d-dimensional stationary Poisson process S ⊂ R d. The algorithm is independent of the origin of coordinates. We show that (1) the graph has one topological end —that is, from any point there is exactly one infinite self-avoiding path; (2) the graph has a unique connected ...

There are three classical algorithms to visit all the nodes of a binary tree – preorder, inorder and postorder traversal. From this one gets a natural labelling of the n internal nodes of a binary tree by the numbers 1; 2; : : : ; n, indicating the sequence in which the nodes are visited. For given n (size of the tree) and j (a number between 1 and n), we consider the statistics number of ascen...

First-order term unification is an essential concept in areas like functional and logic programming, automated deduction, deductive databases, artificial intelligence, information retrieval, compiler design, etc. We build upon recent developments in grammar-based compression mechanisms for terms and investigate algorithms for first-order unification and matching on compressed terms. We prove th...

Groote and Vaandrager introduced the tyft format, which is a congruence format for strong bisimulation equivalence. This article proposes additional syntactic requirements on the tyft format, extended with predicates, to obtain a precongruence format for language preorder.

This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. © 2006 Elsevier B.V. All rights reserved.

This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theo...

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with just a weak test for zero. Unlike many other semantic equivalences, strong and weak simulation preorder are decidable for OCN, but the computational complexity was an open problem. We show that both strong and weak simulation preorder on OCN are PSPACE-complete....

Extended Abstract ABSTRACT We recast Milner's work on nite delay in synchronous CCS by giving a denota-tional semantics for admissibility of innnite computations on a biinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model D K for an operational preorder which generalizes Milner's fortiica-tion and whose restriction to nite behavior corresponds to Abram...

A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves ω-completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, groundand ω-complete axiomatizations are de...