On the unambiguity of n-tuple languages

Several results concerning the preservation of unambiguity in n-tuple languages are presented here. Furthermore, the notion of n-stratified sets — as appropriate generalization of the straified sets defined by Ginsburg — is introduced and a necessary and sufficient characterisation result for bounded unambiguous n-tuple languages analogous to bounded unambiguous context free languages is given.     

How to meet when you forget: log-space rendezvous in arbitrary graphs

Two identical (anonymous) mobile agents start from arbitrary nodes in an a priori unknown graph and move synchronously from node to node with the goal of meeting. This rendezvous problem has been thoroughly studied, both for anonymous and for labeled agents, along with another basic task, that of exploring graphs by mobile agents. The rendezvous problem is known to be not easier than graph exploration. A well-known recent result on exploration, due to Reingold, states that deterministic exploration of arbitrary graphs can be performed in log-space, i.e., using an agent equipped with O(log n) bits of memory, where n is the size of the graph. In this paper we study the size of memory of mobile agents that permits us to solve the rendezvous problem deterministically. Our main result establishes the minimum size of the memory of anonymous agents that guarantees deterministic rendezvous when it is feasible. We show that this minimum size is Θ(log n), where n is the size of the graph, regardless of the delay between the starting times of the agents. More precisely, we construct identical agents equipped with Θ(log n) memory bits that solve the rendezvous problem in all graphs with at most n nodes, if they start with any delay τ, and we prove a matching lower bound Ω(log n) on the number of memory bits needed to accomplish rendezvous, even for simultaneous start. In fact, this lower bound is achieved already on the class of rings. This shows a significant contrast between rendezvous and exploration: e.g., while exploration of rings (without stopping) can be done using constant memory, rendezvous, even with simultaneous start, requires logarithmic memory. As a by-product of our techniques introduced to obtain log-space rendezvous we get the first algorithm to find a quotient graph of a given unlabeled graph in polynomial time, by means of a mobile agent moving around the graph.     

On the power of magic

This paper considers the efficient evaluation of recursive queries expressed using Horn clauses. We define sideways information passing formally and show how a query evaluation algorithm may be defined in terms of sideways information passing and control. We then consider a class of information-passing strategies that suffices to describe most query evaluation algorithms in the database literature, and show that these strategies may always be implemented by rewriting a given program and evaluating the rewritten program bottom-up. We describe in detail several algorithms for rewriting a program. These algorithms generalize the counting and magic-sets algorithms to work with arbitrary programs. Safety and optimality of the algorithms are also considered.     

On the power of randomization in on-line algorithms

Against in adaptive adversary, we show that the power of randomization in on-line algorithms is severely limited! We prove the existence of an efficient simulation of randomized on-line algorithms by deterministic ones, which is best possible in general. The proof of the upper bound is existential. We deal with the issue of computing the efficient deterministic algorithm, and show that this is possible in very general cases.A previous version of this paper appeared in the22nd ACM STOC Conference Proceedings. Part of this research was performed while A. Borodin and A. Wigderson were visitors at the International Computer Science Institute, and while G. Tardos was a visitor at the Hebrew University.     

On the power of L-systems in image generation

Image generation with DOL-systems is discussed. It is shown that, if either the vector or the turtle geometry interpretation is used, DOL-systems can produce step-by-step all images that can be generated by regular languages (or by equivalent Iterative Matrix Homomorphisms of Shallit and Stolfi). An extension of turtle geometry interpretation is introduced that enables L-systems to generate gray-tone images. It is shown that with our extension every Weighted Finite Automaton can be simulated step-by-step by a DOL-system.An abbreviated version of this paper was presented at the conference Developments in Formal Languages, Turku, July 1993.Research supported by the NSF Grant No. CCR-9202396This article was processed by the author using the LATEX style file pljourl from Springer-Verlag.     

On the power of non-local boxes

A non-local box is a virtual device that has the following property: given that Alice inputs a bit at her end of the device and that Bob does likewise, it produces two bits, one at Alice's end and one at Bob's end, such that the XOR of the outputs is equal to the AND of the inputs. This box, inspired from the CHSH inequality, was first proposed by Popescu and Rohrlich to examine the question: given that a maximally entangled pair of qubits is non-local, why is it not maximally non-local? We believe that understanding the power of this box will yield insight into the non-locality of quantum mechanics. It was shown recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able to simulate correlations from any measurement on a singlet state. Here, we show that the non-local box can in fact do much more: through the simulation of the magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we show that the non-local box can simulate quantum correlations that no entangled pair of qubits can, in a bipartite scenario and even in a multi-party scenario. Finally we show that a single non-local box cannot simulate all quantum correlations and propose a generalization for a multi-party non-local box. In particular, we show quantum correlations whose simulation requires an exponential amount of non-local boxes, in the number of maximally entangled qubit pairs.     

On the computational power of winner-take-all

This article initiates a rigorous theoretical analysis of the computational power of circuits that employ modules for computing winner-take-all. Computational models that involve competitive stages have so far been neglected in computational complexity theory, although they are widely used in computational brain models, artificial neural networks, and analog VLSI. Our theoretical analysis shows that winner-take-all is a surprisingly powerful computational module in comparison with threshold gates (also referred to as McCulloch-Pitts neurons) and sigmoidal gates. We prove an optimal quadratic lower bound for computing winner-take-all in any feedforward circuit consisting of threshold gates. In addition we show that arbitrary continuous functions can be approximated by circuits employing a single soft winner-take-all gate as their only nonlinear operation. Our theoretical analysis also provides answers to two basic questions raised by neurophysiologists in view of the well-known asymmetry between excitatory and inhibitory connections in cortical circuits: how much computational power of neural networks is lost if only positive weights are employed in weighted sums and how much adaptive capability is lost if only the positive weights are subject to plasticity.     

On the power of fuzzy logic

In this article we address the issues brought up by Elkan in his article, “The paradoxical success of fuzzy logic,” [IEEE Expert, 3–8 (1994)]. Elkan's work has caused concern since it purportedly reveals a Fuzzy Logic weakness regarding its theoretical foundations. A further investigation of Elkan's theorem (“Theorem 1”) revealed that its conclusion is not correct. After indicating the points where we disagree with Elkan, we reformulate Theorem 1, calling this new version “Theorem 2.” Theorems 1 and 2 have the same hypotheses but different conclusions. According to Theorem 2 there is a region of points that do hold the equivalence in the hypotheses of Theorem 1. In other words, one does not need to change the definition of logical equivalence in Theorem 1 in order to prove that Fuzzy Logic does not collapse to a two-valued logic. In a further analysis of Theorem 2 we show that Elkan's work does not affect the power of Fuzzy Logic to model vagueness. © 1996 John Wiley & Sons, Inc.     

On the power of programming features

We consider the power of several programming features such as counters, pushdown stacks, queues, arrays, recursion and equality. In this study program schemas are used as the model for computation. The relations between the powers of these features is completely described by a comparison diagram.     

On the power of generalized Mod-classes

We investigate the computational power of the new counting class ModP which generalizes the classes Mod _p P,p prime. We show that ModP is polynomialtime truth-table equivalent in power to #P and that ModP is contained in the class AmpMP. As a consequence, the classes PP, ModP, and AmpMP are all Turing equivalent, and thus AmpMP and ModP are not low for MP unless the counting hierarchy collapses to MP. Furthermore, we show that every set in C=P is reducible to some set in ModP via a random many-one reduction that uses only logarithmically many random bits. Hence, ModP and AmpMP are not closed under polynomial-time conjunctive reductions unless the counting hierarchy collapses.     

On the tree-transformation power of XSLT

XSLT is a standard rule-based programming language for expressing transformations of XML data. The language is currently in transition from version 1.0 to 2.0. In order to understand the computational consequences of this transition, we restrict XSLT to its pure tree-transformation capabilities. Under this focus, we observe that XSLT 1.0 was not yet a computationally complete tree-transformation language: every 1.0 program can be implemented in exponential time, using a DAG representation of trees. A crucial new feature of version 2.0, however, which allows node sets over temporary trees, yields completeness. We provide a formal operational semantics for XSLT programs, and establish confluence for this semantics.Wim Janssen is a research assistant of the Fund for Scientific Research, Flanders. Alexandr Korlyukov sadly passed away shortly after we agreed to write a joint paper.     

On the expressive power of schemes

We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike λ-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names are introduced for the hypotheses. We show that despite its non-determinism, some typed scheme-calculi have the same expressivity as the corresponding typed λ-calculi.     

On the unification power of models

In November 2000, the OMG made public the MDAinitiative, a particular variant of a new global trend called MDE (Model Driven Engineering). The basic ideas of MDA are germane to many other approaches such as generative programming, domain specific languages, model-integrated computing, generic model management, software factories, etc. MDA may be defined as the realization of MDE principles around a set of OMG standards like MOF, XMI, OCL, UML, CWM, SPEM, etc. MDE is presently making several promises about the potential benefits that could be reaped from a move from code-centric to model-based practices. When we observe these claims, we may wonder when they may be satisfied: on the short, medium or long term or even never perhaps for some of them. This paper tries to propose a vision of the development of MDE based on some lessons learnt in the past 30 years in the development of object technology. The main message is that a basic principle (Everything is an object) was most helpful in driving the technology in the direction of simplicity, generality and power of integration. Similarly in MDE, the basic principle that Everything is a model has many interesting properties, among others the capacity to generate a realistic research agenda. We postulate here that two core relations (representation and conformance) are associated to this principle, as inheritance and instantiation were associated to the object unification principle in the class-based languages of the 80s. We suggest that this may be most useful in understanding many questions about MDE in general and the MDA approach in particular. We provide some illustrative examples. The personal position taken in this paper would be useful if it could generate a critical debate on the research directions in MDE.     

On the computational power of insertion-deletion systems

Gene insertion and deletion are basic phenomena found in DNA processing or RNA editing in molecular biology. The genetic mechanism and development based on these evolutionary transformations have been formulated as a formal system with two operations of insertion and deletion, called insertion-deletion systems (Kari and Thierrin, 1996; Kari et al., 1997).We investigate the generative power of insertion-deletion systems (InsDel systems), and show that the family INS ¹ ₁ DEL ¹ ₁ is equal to the family of recursively enumerable languages. This gives a positive answer to an open problem posed in Kari et al. (1997) where it was conjectured contrary. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the power of deep pushdown stacks

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, NPSDS _s , based around assignments, while-loops and non-deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of NPSDS _s by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of NPSDS _s are in EXPTIME.     

On the power of randomized multicounter machines

One-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism. For instance, we show that polynomial-time one-way multicounter machines, with error probability tending to zero with growing input length, can recognize languages that cannot be accepted by polynomial-time nondeterministic two-way multicounter machines with a bounded number of reversals. A similar result holds for the comparison of determinism and one-sided-error randomization, and of determinism and Las Vegas randomization.     

On the Expressive Power of F-Logic Language

F-logic language is a logic database language based on frame logic.It is powerful in expressing object-oriented features.However,there was little work discussing its capability of manipulating complex objects.In this paper,the authors compare the capability of F-logic with that of logic database languages represented by COL.Through two pairs of semantic-preserving transformations,F-logic progams and their corresponding Herbrand interpretations,and vice versa.Also,the effects of negation are discussed.The results of this paper indicate that,without consideration of the effects of OID generating,F-logic language has the same power in manipulatin complex objects as COL,LDL1,and ELPS.     

On the expressive power of behavioral profiles

Behavioral profiles have been proposed as a behavioral abstraction of dynamic systems, specifically in the context of business process modeling. A behavioral profile can be seen as a complete graph over a set of task labels, where each edge is annotated with one relation from a given set of binary behavioral relations. Since their introduction, behavioral profiles were argued to provide a convenient way for comparing pairs of process models with respect to their behavior or computing behavioral similarity between process models. Still, as of today, there is little understanding of the expressive power of behavioral profiles. Via counter-examples, several authors have shown that behavioral profiles over various sets of behavioral relations cannot distinguish certain systems up to trace equivalence, even for restricted classes of systems represented as safe workflow nets. This paper studies the expressive power of behavioral profiles from two angles. Firstly, the paper investigates the expressive power of behavioral profiles and systems captured as acyclic workflow nets. It is shown that for unlabeled acyclic workflow net systems, behavioral profiles over a simple set of behavioral relations are expressive up to configuration equivalence. When systems are labeled, this result does not hold for any of several previously proposed sets of behavioral relations. Secondly, the paper compares the expressive power of behavioral profiles and regular languages. It is shown that for any set of behavioral relations, behavioral profiles are strictly less expressive than regular languages, entailing that behavioral profiles cannot be used to decide trace equivalence of finite automata and thus Petri nets.     

On the expressive power of data dependencies

Summary The class of data dependencies is a class of first-order sentences that seem to be suitable to express semantic constraints for relational databases. We deal with the question of which classes of databases are axiomatizable by data dependencies. (A class of databases is said to be axiomatizable by sentences of a certain kind if there exists a set of sentences of that kind such that is the class of all models of that set.) Our results characterize, by algebraic closure conditions, classes of databases that are axiomatizable by dependencies of different kinds. Our technique is model-theoretic, and the characterization easily entails all previously known results on axiomatizability by dependencies.Research partially supported by Swiss National Science Foundation Grant No. 82.820.0.80 (1980–1982), revision of the paper was done while visiting the Mathematisches Forschungsinstitut at the Swiss Federal Institute of Technology (Summer 1985)Part of the research reported here was done while the author was at Stanford University and supported by a Weizmann Post-Doctoral Fellowship and AFOSR grant 80-0212