Interpretation and reduction of attribute grammars

An attribute grammar (AG) is in reduced form if in all its derivation trees every attribute contributes to the translation. We prove that, eventhough AG are generally not in reduced form, they can be reduced, i.e., put into reduced form, without modifying their translations. This is shown first for noncircular AG and then for arbitrary AG. In both cases the reduction consists of easy (almost syntactic) transformations which do not change the semantic domain of the AG. These easy transformations are formalized by introducing the notion of AG interpretation as an extension to AG of the concept of context-free grammar form. Finally we prove that any general algorithm for reducing even the simple class of L-AG needs exponential time (in the size of the input AG) infinitely often

Isomorphism Checking for Symmetry Reduction

In this paper, we show how isomorphism checking can be used as an effective technique for symmetry reduction. Reduced state spaces are equivalent to the original ones under a strong notion of bisimilarity which preserves the multiplicity of outgoing transitions, and therefore also preserves stochastic temporal logics. We have implemented this in a setting where states are arbitrary graphs. Since no efficiently computable canonical representation is known for arbitrary graphs modulo isomorphism, we define an isomorphism-predicting hash function on the basis of an existing partition refinement algorithm. As an example, we report a factorial state space reduction on a model of an ad-hoc network connectivity protocol

Parameterizable Views for Process Visualization

In large organizations different users or user groups usually have distinguished perspectives over business processes and related data. Personalized views on the managed processes are therefore needed. Existing BPM tools, however, do not provide adequate mechanisms for building and visualizing such views. Very often processes are displayed to users in the same way as drawn by the process designer. To tackle this inflexibility this paper presents an advanced approach for creating personalized process views based on well-defined, parameterizable view operations. Respective operations can be flexibly composed in order to reduce or aggregate process information in the desired way. Depending on the chosen parameterization of the applied view operations, in addition, different "quality levels" with more or less relaxed properties can be obtained for the resulting process views (e.g., regarding the correctness of the created process view scheme). This allows us to consider the specific needs of the different applications utilizing process views (e.g., process monitoring tools or process editors). Altogether, the realized view concept contributes to better deal with complex, long-running business processes with hundreds up to thousands of activities

Backwards State-space Reduction for Planning in Dynamic Knowledge Bases

In this paper we address the problem of planning in rich domains, where knowledge representation is a key aspect for managing the complexity and size of the planning domain. We follow the approach of Description Logic (DL) based Dynamic Knowledge Bases, where a state of the world is represented concisely by a (possibly changing) ABox and a (fixed) TBox containing the axioms, and actions that allow to change the content of the ABox. The plan goal is given in terms of satisfaction of a DL query. In this paper we start from a traditional forward planning algorithm and we propose a much more efficient variant by combining backward and forward search. In particular, we propose a Backward State-space Reduction technique that consists in two phases: first, an Abstract Planning Graph P is created by using the Abstract Backward Planning Algorithm (ABP), then the abstract planning graph P is instantiated into a corresponding planning graph P by using the Forward Plan Instantiation Algorithm (FPI). The advantage is that in the preliminary ABP phase we produce a symbolic plan that is a pattern to direct the search of the concrete plan. This can be seen as a kind of informed search where the preliminary backward phase is useful to discover properties of the state-space that can be used to direct the subsequent forward phase. We evaluate the effectiveness of our ABP+FPI algorithm in the reduction of the explored planning domain by comparing it to a standard forward planning algorithm and applying both of them to a concrete business case study.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.Comment: 15page

From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More

We consider questions that arise from the intersection between the areas of polynomial-time approximation algorithms, subexponential-time algorithms, and fixed-parameter tractable algorithms. The questions, which have been asked several times (e.g., [Marx08, FGMS12, DF13]), are whether there is a non-trivial FPT-approximation algorithm for the Maximum Clique (Clique) and Minimum Dominating Set (DomSet) problems parameterized by the size of the optimal solution. In particular, letting $\text{OPT}$ be the optimum and $N$ be the size of the input, is there an algorithm that runs in $t(\text{OPT})\text{poly}(N)$ time and outputs a solution of size $f(\text{OPT})$, for any functions $t$ and $f$ that are independent of $N$ (for Clique, we want $f(\text{OPT})=\omega(1)$)? In this paper, we show that both Clique and DomSet admit no non-trivial FPT-approximation algorithm, i.e., there is no $o(\text{OPT})$-FPT-approximation algorithm for Clique and no $f(\text{OPT})$-FPT-approximation algorithm for DomSet, for any function $f$ (e.g., this holds even if $f$ is the Ackermann function). In fact, our results imply something even stronger: The best way to solve Clique and DomSet, even approximately, is to essentially enumerate all possibilities. Our results hold under the Gap Exponential Time Hypothesis (Gap-ETH) [Dinur16, MR16], which states that no $2^{o(n)}$-time algorithm can distinguish between a satisfiable 3SAT formula and one which is not even $(1 - \epsilon)$-satisfiable for some constant $\epsilon > 0$. Besides Clique and DomSet, we also rule out non-trivial FPT-approximation for Maximum Balanced Biclique, Maximum Subgraphs with Hereditary Properties, and Maximum Induced Matching in bipartite graphs. Additionally, we rule out $k^{o(1)}$-FPT-approximation algorithm for Densest $k$-Subgraph although this ratio does not yet match the trivial $O(k)$-approximation algorithm.Comment: 43 pages. To appear in FOCS'1