Showing papers on "Recursively enumerable language published in 2009"

Generalized schema-mappings: from termination to tractability

Abstract: Data-Exchange is the problem of creating new databases according to a high-level specification called a schema-mapping while preserving the information encoded in a source database. This paper introduces a notion of generalized schema-mapping that enriches the standard schema-mappings (as defined by Fagin et al) with more expressive power. It then proposes a more general and arguably more intuitive notion of semantics that rely on three criteria: Soundness, Completeness and Laconicity (non-redundancy and minimal size). These semantics are shown to coincide precisely with the notion of cores of universal solutions in the framework of Fagin, Kolaitis and Popa. It is also well-defined and of interest for larger classes of schema-mappings and more expressive source databases (with null-values and equality constraints). After an investigation of the key properties of generalized schema-mappings and their semantics, a criterion called Termination of the Oblivious Chase (TOC) is identified that ensures polynomial data-complexity. This criterion strictly generalizes the previously known criterion of Weak-Acyclicity. To prove the tractability of TOC schema-mappings, a new polynomial time algorithm is provided that, unlike the algorithm of Gottlob and Nash from which it is inspired, does not rely on the syntactic property of Weak-Acyclicity. As the problem of deciding whether a Schema-mapping satisfies the TOC criterion is only recursively enumerable, a more restrictive criterion called Super-weak Acylicity (SwA) is identified that can be decided in Polynomial-time while generalizing substantially the notion of Weak-Acyclicity.

The Computational Geometry of Comparing Shapes

Abstract: This article is a survey on methods from computational geometry for comparing shapes that we developed within our work group at Freie Universitat Berlin. In particular, we will present the ideas and complexity considerations for the computation of two distance measures, the Hausdorff distance and the Frechet distance. Whereas the former is easier to compute, the latter better captures the similarity of shapes as perceived by human observers. We will consider shapes modelled by curves in the plane as well as surfaces in three-dimensional space. Especially, the Frechet distance of surfaces seems computationally intractable and is of yet not even known to be computable. At least the decision problem is shown to be recursively enumerable.

Mathematical foundations of computer science 2009 : 34th International Symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009 : proceedings

Abstract: Invited Papers.- Four Subareas of the Theory of Constraints, and Their Links.- Synchronization of Regular Automata.- Stochastic Process Creation.- Stochastic Games with Finitary Objectives.- Stochastic Data Streams.- Recent Advances in Population Protocols.- How to Sort a Train.- Contributed Papers.- Arithmetic Circuits, Monomial Algebras and Finite Automata.- An Improved Approximation Bound for Spanning Star Forest and Color Saving.- Energy-Efficient Communication in Multi-interface Wireless Networks.- Private Capacities in Mechanism Design.- Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules.- Sampling Edge Covers in 3-Regular Graphs.- Balanced Paths in Colored Graphs.- Few Product Gates But Many Zeros.- Branching Programs for Tree Evaluation.- A Dichotomy Theorem for Polynomial Evaluation.- DP-Complete Problems Derived from Extremal NP-Complete Properties.- The Synchronization Problem for Locally Strongly Transitive Automata.- Constructing Brambles.- Self-indexed Text Compression Using Straight-Line Programs.- Security and Tradeoffs of the Akl-Taylor Scheme and Its Variants.- Parameterized Complexity Classes under Logical Reductions.- The Communication Complexity of Non-signaling Distributions.- How to Use Spanning Trees to Navigate in Graphs.- Representing Groups on Graphs.- Admissible Strategies in Infinite Games over Graphs.- A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems.- Future-Looking Logics on Data Words and Trees.- A By-Level Analysis of Multiplicative Exponential Linear Logic.- Hyper-minimisation Made Efficient.- Regular Expressions with Counting: Weak versus Strong Determinism.- Choosability of P 5-Free Graphs.- Time-Bounded Kolmogorov Complexity and Solovay Functions.- The Longest Path Problem Is Polynomial on Interval Graphs.- Synthesis for Structure Rewriting Systems.- On the Hybrid Extension of CTL and CTL?+?.- Bounds on Non-surjective Cellular Automata.- FO Model Checking on Nested Pushdown Trees.- The Prismoid of Resources.- A Dynamic Algorithm for Reachability Games Played on Trees.- An Algebraic Characterization of Semirings for Which the Support of Every Recognizable Series Is Recognizable.- Graph Decomposition for Improving Memoryless Periodic Exploration.- On FO 2 Quantifier Alternation over Words.- On the Recognizability of Self-generating Sets.- The Isomorphism Problem for k-Trees Is Complete for Logspace.- Snake-Deterministic Tiling Systems.- Query Automata for Nested Words.- A General Class of Models of .- The Complexity of Satisfiability for Fragments of Hybrid Logic-Part I.- Colouring Non-sparse Random Intersection Graphs.- On the Structure of Optimal Greedy Computation (for Job Scheduling).- A Probabilistic PTAS for Shortest Common Superstring.- The Cost of Stability in Network Flow Games.- (Un)Decidability of Injectivity and Surjectivity in One-Dimensional Sand Automata.- Quantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm.- From Parity and Payoff Games to Linear Programming.- Partial Randomness and Dimension of Recursively Enumerable Reals.- Partial Solution and Entropy.- On Pebble Automata for Data Languages with Decidable Emptiness Problem.- Size and Energy of Threshold Circuits Computing Mod Functions.- Points on Computable Curves of Computable Lengths.- The Expressive Power of Binary Submodular Functions.

Cellular Automata and Language Theory.

Abstract: Cellular automaton A (one-dimensional) cellular automaton is a linear array of cells which are connected to both of their nearest neighbors. The total number of cells in the array is determined by the input data. They are exactly in one of a finite number of states, which is changed according to local rules depending on the current state of a cell itself and the current states of its neighbors. The state changes take place simultaneously at discrete time steps. The input mode for cellular automata is called parallel. One can suppose that all cells fetch their input symbol during a pre-initial step. Iterative array Basically, iterative arrays are cellular automata whose leftmost cell is distinguished. This socalled communication cell is connected to the input supply and fetches the input sequentially. The cells are initially empty, that is, in a special quiescent state. Formal language The data on which the devices operate are strings built from input symbols of a finite set or alphabet. A subset of strings over a given alphabet is a formal language. Signal Signals are used to transmit and encode information in cellular automata. If a cell changes to the state of its neighbor after some k time steps, and if subsequently its neighbors and their neighbors do the same, then the basic signal moves with speed k through the array. With the help of auxiliary signals, rather complex signals can be established. Closure property Closure properties of families of formal languages indicate their robustness under certain operations. A family of formal languages is closed under some operation, if any application of the operation on languages from the family yields again a language from the family. Turing machine A Turing machine is the simplest form of a universal computer. It captures the idea of an effective procedure or algorithm. At any time the machine is in any one of a finite number of states. It is equipped with an infinite tape divided into cells and a read-write head scanning a single cell. Each cell may contain a symbol from a finite set or alphabet. Initially, the finite input is written in successive cells. All other cells are empty. Dependent on a list of instructions, which serve as the program for the machine, the action is determined completely by the current state and the symbol currently scanned by the head. The action comprises the symbol to be written on the current cell, the new state of the machine, and the information of whether the head should move left or right. Decidability A formal problem with two alternatives is decidable, if there is an algorithm or a Turing machine that solves it and halts on all inputs. That is, given an encoding of some instance of the problem, the algorithm or Turing machine returns the correct answer yes or no. The problem is semidecidable, if the algorithm halts on all instances for which the answer is yes.

Can We Compute the Similarity between Surfaces

Abstract: A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Frechet distance. Whereas efficient algorithms are known for computing the Frechet distance of polygonal curves, the same problem for triangulated surfaces is NP-hard. Furthermore, it remained open whether it is computable at all. Using a discrete approximation, we show that it is upper semi-computable, i.e., there is a non-halting Turing machine which produces a decreasing sequence of rationals converging to the Frechet distance. It follows that the decision problem, whether the Frechet distance of two given surfaces lies below a specified value, is recursively enumerable. Furthermore, we show that a relaxed version of the Frechet distance, the weak Frechet distance can be computed in polynomial time. For this, we give a computable characterization of the weak Frechet distance in a geometric data structure called the Free Space Diagram.

On finitely recursive programs

Abstract: Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable model semantics is highly undecidable. In this paper we prove that a larger class of programs, called finitely recursive programs, preserves most of the good properties of finitary programs under the stable model semantics, namely: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: We prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting omega-sequence converge to a stable model of P.

On finitely recursive programs1

Abstract: Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties; for example, ground queries are decidable, while in the general case the stable model semantics are Π11-hard. In this paper we prove that a larger class of programs, called finitely recursive programs, preserve most of the good properties of finitary programs under the stable model semantics, which are as follows: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: we prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting ω-sequence converge to a stable model of P.

On Networks of Evolutionary Processors with Nodes of Two Types

Abstract: We discuss the power of networks of evolutionary processors where only two types of nodes are allowed. We prove that (up to an intersection with a monoid) every recursively enumerable language can be generated by a network with one deletion and one insertion node. Networks with an arbitrary number of deletion and substitution nodes only produce finite languages, and for each finite language one deletion node or one substitution node is sufficient. Networks with an arbitrary number of insertion and substitution nodes only generate context-sensitive languages, and (up to an intersection with a monoid) every context-sensitive language can be generated by a network with one substitution node and one insertion node. All results are optimal with respect to the number of nodes.

P Systems with Minimal Insertion and Deletion

Abstract: In this paper, we consider insertion-deletion P systems with priority of deletion over insertion. We show that such systems with one-symbol context-free insertion and deletion rules are able to generate Parikh sets of all recursively enumerable languages (PsRE). If a one-symbol one-sided context is added to the insertion or deletion rules, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important, and in its absence the corresponding class of P systems is strictly included in the family of matrix languages (MAT).

Enumerating limit groups

Abstract: We prove that the set of limit groups is recursively enumerable, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore, there exists an algorithm that computes presentations for finitely generated subgroups. The other main ingredient is the ability to algorithmically calculate centralizers in relatively hyperbolic groups. Applications include the existence of recognition algorithms for limit groups and free groups.

A course in formal languages, automata and groups

Abstract: The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in this developing field. The first three Chapters give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter Four covers the context-free languages, whereas Chapter Five clarifies the relationship between LR(k) languages and deterministic (context-free languages). Chiswell's book is unique in that it gives the reader a thorough introduction into the connections between group theory and formal languages. This information, contained within the final chapter, includes work on the Anisimov and Muller-Schupp theorems.

Computational Power of P Systems with Small Size Insertion and Deletion Rules

Abstract: Recent investigations show insertion-deletion systems of small size that are not complete and cannot generate all recursively enumerable languages. However, if additional computational distribution mechanisms like P systems are added, then the computational completeness is achieved in some cases. In this article we take two insertion-deletion systems that are not computationally complete, consider them in the framework of P systems and show that the computational power is strictly increased by proving that any recursively enumerable language can be generated. At the end some open problems are presented.

Turing degrees and the ershov hierarchy

Abstract: An n-r.e. set can be defined as the symmetric difference of n recursively enumerable sets. The classes of these sets form a natural hierarchy which became a well-studied topic in recursion theory. In a series of ground-breaking papers, Ershov generalized this hierarchy to transfinite levels based on Kleene’s notations of ordinals and this work lead to a fruitful study of these sets and their many-one and Turing degrees. The Ershov hierarchy is a natural measure of complexity of the sets below the halting problem. In this paper, we survey the early work by Ershov and others on this hierarchy and present the most fundamental results. We also provide some pointers to concurrent work in the field.

Kleene monads: handling iteration in a framework of generic effects

Abstract: Monads are a well-established tool for modelling various computational effects. They form the semantic basis of Moggi's computational metalanguage, the metalanguage of effects for short, which made its way into modern functional programming in the shape of Haskell's do-notation. Standard computational idioms call for specific classes of monads that support additional control operations. Here, we introduce Kleene monads, which additionally feature nondeterministic choice and Kleene star, i.e. nondeterministic iteration, and we provide a metalanguage and a sound calculus for Kleene monads, the metalanguage of control and effects, which is the natural joint extension of Kleene algebra and the metalanguage of effects. This provides a framework for studying abstract program equality focussing on iteration and effects. These aspects are known to have decidable equational theories when studied in isolation. However, it is well known that decidability breaks easily; e.g. the Horn theory of continuous Kleene algebras fails to be recursively enumerable. Here, we prove several negative results for the metalanguage of control and effects; in particular, already the equational theory of the unrestricted metalanguage of control and effects over continuous Kleene monads fails to be recursively enumerable. We proceed to identify a fragment of this language which still contains both Kleene algebra and the metalanguage of effects and for which the natural axiomatisation is complete, and indeed the equational theory is decidable.

The $\Pi^0_2$-Completeness of Most of the Properties of Rewriting Systems You Care About (and Productivity)

Abstract: Most of the standard pleasant properties of term rewriting systems are undecidable; to wit: local confluence, confluence, normalization, termination, and completeness. Mere undecidability is insufficient to rule out a number of possibly useful properties: For instance, if the set of normalizing term rewriting systems were recursively enumerable, there would be a program yielding "yes" in finite time if applied to any normalizing term rewriting system. The contribution of this paper is to show (the uniform version of) each member of the list of properties above (as well as the property of being a productive specification of a stream) complete for the class $\Pi^0_2$. Thus, there is neither a program that can enumerate the set of rewriting systems enjoying any one of the properties, nor is there a program enumerating the set of systems that do not. For normalization and termination we show both the ordinary version and the ground versions (where rules may contain variables, but only ground terms may be rewritten) $\Pi^0_2$-complete. For local confluence, confluence and completeness, we show the ground versions $\Pi^0_2$-complete.

Incompatible Ω-complete theories

Abstract: In 1985 the second author showed that if there is a proper class of measurable Woodin cardinals and V𝔹1 and V𝔹2 are generic extensions of V satisfying CH then V𝔹1 and V𝔹2 agree on all Σ21-statements. In terms of the strong logic Ω-logic this can be reformulated by saying that under the above large cardinal assumption ZFC + CH is Ω-complete for Σ21. Moreover, CH is the unique Σ21-statement with this feature in the sense that any other Σ21-statement with this feature is Ω-equivalent to CH over ZFC. It is natural to look for other strengthenings of ZFC that have an even greater degree of Ω-completeness. For example, one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for all of third-order arithmetic. Going further, for each specifiable segment Vλ of the universe of sets (for example, one might take Vλ to be the least level that satisfies there is a proper class of huge cardinals), one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for the theory of Vλ. If such theories exist, extend one another, and are unique in the sense that any other such theory B with the same level of Ω-completeness as A is actually Ω-equivalent to A over ZFC, then this would show that there is a unique Ω-complete picture of the successive fragments of the universe of sets and it would make for a very strong case for axioms complementing large cardinal axioms. In this paper we show that uniqueness must fail. In particular, we show that if there is one such theory that Ω-implies CH then there is another that Ω-implies ¬CH.

On the Power of Insertion P Systems of Small Size

Abstract: In this article we investigate insertion systems of small size in the framework of P systems. We consider P systems with insertion rules having one symbol context and we show that they have the computational power of matrix grammars. If contexts of length two are permitted, then any recursively enumerable language can be generated. In both cases an inverse morphism and a weak coding were applied to the output of the corresponding P systems.

New Morphic Characterizations of Languages in Chomsky Hierarchy Using Insertion and Locality

Abstract: In this paper, we obtain some characterizations and representation theorems of languages in Chomsky hierarchy by using insertion systems, strictly locally testable languages, and morphisms. For instance, each recursively enumerable language L can be represented in the form L = h (L (*** ) *** R ), where *** is an insertion system of weight (3,3), R is a strictly 2-testable language, and h is a projection. A similar representation can be obtained for context-free languages, using insertion systems of weight (3,0) and strictly 4-testable languages, as well as for regular languages, using insertion systems of weight (1,0) and strictly 2-testable languages.

Cooperating distributed grammar systems with permitting grammars as components

Abstract: This paper studies cooperating distributed grammar systems working in the terminal derivation mode where the components are variants of permitting grammars. It proves that although the family of permitting languages is strictly included in the family of random context languages, the families of random context languages and languages generated by permitting cooperating distributed grammar systems in the above mentioned derivation mode coincide. Moreover, if the components are so-called left-permitting grammars, then cooperating distributed grammar systems in the terminal mode characterize the class of context-sensitive languages, or if erasing rules are allowed, the class of recursively enumerable languages. Descriptional complexity results are also presented. It is shown that the number of permitting components can be bounded, in the case of left-permitting components with erasing rules even together with the number of nonterminals.

Elements of Computation Theory

Abstract: Mathematical Preliminaries.- Regular Languages.- Equivalences.- Structure of Regular Languages.- Context-free Languages.- Structure of CFLs.- Recursively Enumerable Languages.- A Non-recursively Enumerable Language.- Algorithmic Solvability.- Computational Complexity.

DNA splicing: computing by observing

Abstract: Motivated by several techniques for observing molecular processes in real-time we introduce a computing device that stresses the role of the observer in biological computations and that is based on the observed behavior of a splicing system. The basic idea is to introduce a marked DNA strand into a test tube with other DNA strands and restriction enzymes. Under the action of these enzymes the DNA starts to splice. An external observer monitors and registers the evolution of the marked DNA strand. The input marked DNA strand is then accepted if its observed evolution follows a certain expected pattern. We prove that using simple observers (finite automata), applied on finite splicing systems (finite set of rules and finite set of axioms), the class of recursively enumerable languages can be recognized.

Bounding non-GL 2 and R.E.A.

Abstract: We prove that every degree a bounding some non-GL2 degree is recursively enumerable in and above (r.e.a.) some 1-generic de-

Partial Randomness and Dimension of Recursively Enumerable Reals

Abstract: A real α is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to α. It is known that the randomness of an r.e. real α can be characterized in various ways using each of the notions; program-size complexity, Martin-Lof test, Chaitin Ω number, the domination and Ω-likeness of α, the universality of a computable, increasing sequence of rationals which converges to α, and universal probability. In this paper, we generalize these characterizations of randomness over the notion of partial randomness by parameterizing each of the notions above by a real T C (0,1], where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. As a result, we present ten equivalent characterizations of the partial randomness of an r.e. real. The resultant characterizations of partial randomness are powerful and have many important applications. One of them is to present equivalent characterizations of the dimension of an individual r.e. real. The equivalence between the notion of Hausdorff dimension and compression rate by program-size complexity (or partial randomness) has been established at present by a series of works of many researchers over the last two decades. We present ten equivalent characterizations of the dimension of an individual r.e. real.

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Abstract: Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors.

Effective λ-models versus recursively enumerable λ-theories

Abstract: A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (re for short) We introduce a notion of effective model of λ-calculus, which covers, in particular, all the models individually introduced in the literature We prove that the order theory of an effective model is never re; from this it follows that its equational theory cannot be λβ or λβη We then show that no effective model living in the stable or strongly stable semantics has an re equational theory For Scott's semantics, we investigate the class of graph models and prove that no order theory of a graph model can be re, and that there exists an effective graph model whose equational/order theory is the minimum among the theories of graph models Finally, we show that the class of graph models enjoys a kind of downwards Lowenheim–Skolem theorem

On the Size Complexity of Non-Returning Context-Free PC Grammar Systems

Abstract: Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six contextfree components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the number of nonterminals are limited by certain constants, and these size parameters do not depend on the generated language.