3,049 research outputs found

    Decision problems for node label controlled graph grammars

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    AbstractTwo basic techniques are presented to show the decidability status of a number of problems concerning node label controlled graph grammars. Most of the problems are of graph-theoretic nature and concern topics like planarity, connectedness and bounded degreeness of graph languages

    A multi-agent system in education facility design

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    This paper deals with a multi-agent system which supports the designer in solving complex design tasks. The behaviour of design agents is modelled by sets of grammar rules. Each agent uses a graph grammar or a shape grammar and a database of facts concerning the subtask it is responsible for. The course of the design process is determined by the interaction between specialised agents. Space layouts of designs are represented by attributed graphs encoding both topological structures and semantic properties of solutions. The agents work in parallel on the common graph, independently generating layouts of different design components while specified node labels evoke agents using shape grammars. The agents’ cooperation allows them to combine a form-oriented approach with a functional-structural one in the design process, where the agents generate the general 3D form of the object based on design requirements together with the space layout based on the functional aspects of the solution. Based on the given design criteria, the agents search for admissible solutions within the design space that constitutes their operating environment. The proposed approach is illustrated by the example of designing kindergarten facilities

    Graph Interpolation Grammars: a Rule-based Approach to the Incremental Parsing of Natural Languages

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    Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a syntactic representation of a sentence as each successive lexeme is read. A GIG rule specifies a set of parse configurations that trigger its application and an operation to perform on a matching configuration. Rules are partly context-sensitive; furthermore, they are reversible, meaning that their operations can be undone, which allows the parsing process to be nondeterministic. These two factors confer enough expressive power to the formalism for parsing natural languages.Comment: 41 pages, Postscript onl

    Equilibria, Fixed Points, and Complexity Classes

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    Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or more) players. This paper reviews the underlying computational principles and the corresponding classes

    On the complexity of graph grammars

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    FEAT-REP : representing features in CAD/CAM

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    When CAD/CAM experts view a workpiece, they perceive it in terms of their own expertise. These terms, called features, which are build upon a syntax (geometry) and a semantic (e.g. skeletal plans in manufacturing or functional relations in design), provide an abstraction mechanism to facilitate the creation, manufacturing and analysis of workpieces. Our goal is to enable experts to represent their own feature-language via a feature-grammar in the computer to build feature-based systems e.g. CAPP systems. The application of formal language terminology to the feature definitions facilitates the use of well-known formal language methods in conjunction with our flexible knowledge representation formalism FEAT-REP which will be presented in this paper

    An approach to computing downward closures

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    The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom

    Qualitative Multi-Objective Reachability for Ordered Branching MDPs

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    We study qualitative multi-objective reachability problems for Ordered Branching Markov Decision Processes (OBMDPs), or equivalently context-free MDPs, building on prior results for single-target reachability on Branching Markov Decision Processes (BMDPs). We provide two separate algorithms for "almost-sure" and "limit-sure" multi-target reachability for OBMDPs. Specifically, given an OBMDP, A\mathcal{A}, given a starting non-terminal, and given a set of target non-terminals KK of size k=∣K∣k = |K|, our first algorithm decides whether the supremum probability, of generating a tree that contains every target non-terminal in set KK, is 11. Our second algorithm decides whether there is a strategy for the player to almost-surely (with probability 11) generate a tree that contains every target non-terminal in set KK. The two separate algorithms are needed: we show that indeed, in this context, "almost-sure" ≠\not= "limit-sure" for multi-target reachability, meaning that there are OBMDPs for which the player may not have any strategy to achieve probability exactly 11 of reaching all targets in set KK in the same generated tree, but may have a sequence of strategies that achieve probability arbitrarily close to 11. Both algorithms run in time 2O(k)⋅∣A∣O(1)2^{O(k)} \cdot |\mathcal{A}|^{O(1)}, where ∣A∣|\mathcal{A}| is the total bit encoding length of the given OBMDP, A\mathcal{A}. Hence they run in polynomial time when kk is fixed, and are fixed-parameter tractable with respect to kk. Moreover, we show that even the qualitative almost-sure (and limit-sure) multi-target reachability decision problem is in general NP-hard, when the size kk of the set KK of target non-terminals is not fixed.Comment: 47 page
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