Jan K. Pachl

Uniform self-stabilizing rings

A <italic>self-stabilizing system</italic> has the property that, no matter how it is perturbed, it eventually returns to a legitimate configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors in his 1974 <italic>Communications of the ACM</italic> paper. His solutions use a distinguished processor in the ring, which effectively acts as a controlling element to drive the system toward stability. Dijkstra has observed that a distinguished processor is essential if the number of processors in the ring is composite. We show, by presenting a protocol and proving its correctness, that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. The basic protocol uses &THgr; (<italic>n</italic><supscrpt>2</supscrpt>) states in each processor when <italic>n</italic> is the size of the ring. We modify the basic protocol to obtain one that uses &THgr; (<italic>n</italic><supscrpt>2</supscrpt>/ln <italic>n</italic>) states.

On the limit sets of cellular automata

The limit sets of cellular automata, defined by Wolfram, play an important role in applications of cellular automata to complex systems. A number of results on limit sets are proved, considering both finite and infinite configurations of cellular automata. The main concern of this paper is with testing membership and (essential) emptiness of limit sets for linear and two-dimensional cellular automata.

A distributed system architecture for a distributed application environment

Advances in communications technology, development of powerful desktop workstations, and increased user demands for sophisticated applications are rapidly changing computing from a traditional centralized model to a distributed one. The tools and services for supporting the design, development, deployment, and management of applications in such an environment must change as well. This paper is concerned with the architecture and framework of services required to support distributed applications through this evolution to new environments. In particular, the paper outlines our rationale for a peer-to-peer view of distributed systems, presents motivation for our research directions, describes an architecture, and reports on some preliminary experiences with a prototype system.

A simple proof of a completeness result for leads-to in the UNITY logic

Abstract Jutla, Knapp and Rao (in: Proc. 8th Ann. Symp. on Principles of Distributed Computing ) proved a completeness result for leads-to in UNITY, using their definition of leads-to by means of a predicate-transformer; the proof relies on theorems of temporal logic and μ-calculus. Sanders ( Formal Aspects of Computing 3 (1991) 189–205) defined leads-to in a version of the UNITY logic that incorporates initial conditions, and derived the completeness of temporal logic. The present paper contains a simple direct proof of the same result.

A lower bound for probabilistic distributed algorithms

Abstract The main contribution of the paper is a negative result about probabilistic algorithms: In terms of the number of transmitted messages, the probabilistic distributed algorithms to find the maximum label in every asynchronous unidirectional ring configuration are not more efficient than deterministic (nonprobabilistic) algorithms.

A robust ring transmission protocol

Abstract A ring network consists of a number of stations connected by unidirectional communication channels in a circular configuration: a block of data may be transmitted in the frame that circulates around the ring, and retrieved by the destination station. This paper first reviews the problems in resolving contention among transmitters in the presence of transmission errors. Several solutions are then described, which, unlike the common full/empty-bit scheme, require no centralized error recovery. It is also shown that the solutions can be implemented with minimum station delays.

The per-process view of naming and remote execution

The per-process approach lets each process create its own private view of naming, instead of relying solely on the systems naming tree as in the per-system approach. The result is a flexible naming environment for distributed systems, especially for remote execution.<<ETX>>

Equivalence problems for mappings on infinite strings

This paper is concerned with sets of infinite strings (ω-languages) and mappings between them. The main result is that there is an algorithm for testing the (string by string) equality of two homomorphisms on an ω-regular set of infinite strings. As a corollary we show that it is decidable whether two functional finite-state transducers define the same function on infinite strings (are ω-equivalent).

Wang tilings and distributed verification on anonymous torus networks

Considern2 processors arranged in ann × n torus network in which each processor is connected by direct communication channels with its four neighbours. This paper studies the followingverification problem on anonymousn × n torus networks: verify whether the network is oriented; that is, verify whether there is an agreement, among all processors, on a consistent channel labelling. The problem is to be solved by a distributed algorithm executed by the processors themselves.If processors can label their channels arbitrarily, then there are network labellings that are not oriented but, to the processors, are indistinguishable from ones that are oriented. Hence there is no deterministic distributed verification algorithm. However, a verification algorithm does exist if the initial labellings are suitably restricted. We describe the restrictions placed on the initial labellings by subsets of the permutation groupS4.We show that the existence of an algorithm for verification is equivalent to the existence of certain tilings of the torus with Wang tiles. Using this equivalence, we have determined the existence of a distributed algorithm for the verification problem for alln × n torus networks for an important class of restrictions, the subgroups ofS4.

Finding pseudoperipheral nodes in graphs

The SPARSPAK [5] algorithm for finding pseudoperipheral nodes in graphs with n nodes and e edges has the worst case time complexity Ω(e ,√n). The function e √n is also an asymptotic upper bound for the worst case time complexity of the problem of finding pseudoperipheral nodes.