Sublinearly space bounded iterative arrays

Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio

On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published in the the Proceedings of TACAS 2007, LNCS 442

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

A unified view of parameterized verification of abstract models of broadcast communication

We give a unified view of different parameterized models of concurrent and distributed systems with broadcast communication based on transition systems. Based on the resulting formal models, we discuss related verification methods and tools based on abstractions and symbolic state exploration

Synthesis, structure and power of systolic computations

AbstractA variety of problems related to systolic architectures, systems, models and computations are discussed. The emphases are on theoretical problems of a broader interest. Main motivations and interesting/important applications are also presented. The first part is devoted to problems related to synthesis, transformations and simulations of systolic systems and architectures. In the second part, the power and structure of tree and linear array computations are studied in detail. The goal is to survey main research directions, problems, methods and techniques in not too formal a way

Parameterized verification

The goal of parameterized verification is to prove the correctness of a system specification regardless of the number of its components. The problem is of interest in several different areas: verification of hardware design, multithreaded programs, distributed systems, and communication protocols. The problem is undecidable in general. Solutions for restricted classes of systems and properties have been studied in areas like theorem proving, model checking, automata and logic, process algebra, and constraint solving. In this introduction to the special issue, dedicated to a selection of works from the Parameterized Verification workshop PV \u201914 and PV \u201915, we survey some of the works developed in this research area

Cellular automata with limited inter-cell bandwidth

AbstractA d-dimensional cellular automaton is a d-dimensional grid of interconnected interacting finite automata. There are models with parallel and sequential input modes. In the latter case, the distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as an iterative array. In this paper, d-dimensional iterative arrays and one-dimensional cellular automata are investigated which operate in real and linear time and whose inter-cell communication bandwidth is restricted to some constant number of different messages independent of the number of states. It is known that even one-dimensional two-message iterative arrays accept rather complicated languages such as {ap∣p prime} or {a2n∣n∈N} (H. Umeo, N. Kamikawa, Real-time generation of primes by a 1-bit-communication cellular automaton, Fund. Inform. 58 (2003) 421–435). Here, the computational capacity of d-dimensional iterative arrays with restricted communication is investigated and an infinite two-dimensional hierarchy with respect to dimensions and messages is shown. Furthermore, the computational capacity of the one-dimensional devices in question is compared with the power of two-way and one-way cellular automata with restricted communication. It turns out that the relations between iterative arrays and cellular automata are quite different from the relations in the unrestricted case. Additionally, an infinite strict message hierarchy for real-time two-way cellular automata is obtained as well as a very dense time hierarchy for k-message two-way cellular automata. Finally, the closure properties of one-dimensional iterative arrays with restricted communication are investigated and differences to the unrestricted case are shown as well

Dataflow Programming Paradigms for Computational Chemistry Methods

The transition to multicore and heterogeneous architectures has shaped the High Performance Computing (HPC) landscape over the past decades. With the increase in scale, complexity, and heterogeneity of modern HPC platforms, one of the grim challenges for traditional programming models is to sustain the expected performance at scale. By contrast, dataflow programming models have been growing in popularity as a means to deliver a good balance between performance and portability in the post-petascale era. This work introduces dataflow programming models for computational chemistry methods, and compares different dataflow executions in terms of programmability, resource utilization, and scalability. This effort is driven by computational chemistry applications, considering that they comprise one of the driving forces of HPC. In particular, many-body methods, such as Coupled Cluster methods (CC), which are the gold standard to compute energies in quantum chemistry, are of particular interest for the applied chemistry community. On that account, the latest development for CC methods is used as the primary vehicle for this research, but our effort is not limited to CC and can be applied across other application domains. Two programming paradigms for expressing CC methods into a dataflow form, in order to make them capable of utilizing task scheduling systems, are presented. Explicit dataflow, is the programming model where the dataflow is explicitly specified by the developer, is contrasted with implicit dataflow, where a task scheduling runtime derives the dataflow. An abstract model is derived to explore the limits of the different dataflow programming paradigms