For some computational problems (e.g., product configuration, planning, diagnosis, query answering, phylogeny reconstruction) computing a set of similar diverse solutions may be desirable for better decision-making. With this motivation, we studied several decision optimization versions of this problem in the context of Answer Set Programming (ASP), analyzed their computational complexity, and introduced offline online methods to compute similar diverse solutions of such computational problems with respect to a given distance function. All these methods rely on the idea of computing solutions to a problem by means of finding the answer sets for an ASP program that describes the problem. The offline methods compute all solutions in advance using the ASP formulation of the problem with an ASP solver, like Clasp, and then identify similar diverse solutions using clustering methods. The online methods compute similar diverse solutions following one of the three approaches: by reformulating the ASP representation of the problem to compute similar diverse solutions at once using an ASP solver; by computing similar diverse solutions iteratively (one after other) using an ASP solver; by modifying the search algorithm of an ASP solver to compute similar diverse solutions incrementally. We modified Clasp to implement the last online method and called it Clasp-NK. In the first two online methods, the given distance function is represented in ASP; in the last one it is implemented in C++. We showed the applicability and the effectiveness of these methods on reconstruction of similar diverse phylogenies for Indo-European languages, and on several planning problems in Blocks World. We observed that in terms of computational efficiency the last online method outperforms the others; also it allows us to compute similar diverse solutions when the distance function cannot be represented in ASP.
ASP-based methods for computing similar diverse or close distant solutions to a given problem are probably most useful for existing well-studied ASP applications, such as phylogeny reconstruction @cite_48 @cite_29 or product configuration @cite_10 , to be used with domain-specific measures.
@cite_48 @cite_29 @cite_10
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We introduce a comprehensive framework for computing diverse (or similar) solutions to logic programs with preferences. Our framework provides a wide spectrum of complete and incomplete methods for solving this task. Apart from proposing several new methods, it also accommodates existing ones and generalizes them to programs with preferences. Interestingly, this is accomplished by integrating and automating several basic ASP techniques - being of general interest even beyond diversification. The enabling factor of this lies in the recent advance of multi-shot ASP solving that provides us with fine-grained control over reasoning processes and abolishes the need for solver modifications and wrappers that were indispensable in previous approaches. Our framework is implemented as an extension to the ASP-based preference handling system asprin. We use the resulting system asprin 2 for an empirical evaluation of the diversification methods comprised in our framework. Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity. In answer-set programming (ASP), the main focus usually is on computing answer sets which correspond to solutions to the problem represented by a logic program. Simple reasoning over answer sets is sometimes supported by ASP systems (usually in the form of computing brave or cautious consequences), but slightly more involved reasoning problems require external postprocessing. Generally speaking, it is often desirable to use (a subset of) brave or cautious consequences of a program P 1 as input to another program P 2 in order to provide the desired solutions to the problem to be solved. In practice, the evaluation of the program P 1 currently has to be decoupled from the evaluation of P 2 using an intermediate step which collects the desired consequences of P 1 and provides them as input to P 2 . In this work, we present a novel method for representing such a procedure within a single program, and thus within the realm of ASP itself. Our technique relies on rewriting P 1 into a so-called manifold program , which allows for accessing all desired consequences of P 1 within a single answer set. Then, this manifold program can be evaluated jointly with P 2 avoiding any intermediate computation step. For determining the consequences within the manifold program we use weak constraints , which is strongly motivated by complexity considerations. As an application, we present an encoding for computing the ideal extension of an abstract argumentation framework. Many classes of applications, especially in the domains of signal and image processing, computer graphics, computer vision, and machine learning, are inherently tolerant to inaccuracies in their underlying computations. This tolerance can be exploited to design approximate circuits that perform within acceptable accuracies but have much lower power consumption and smaller area footprints (and often better run times) than their exact counterparts. In this paper, we propose a new class of automated synthesis methods for generating approximate circuits directly from behavioral-level descriptions. In contrast to previous methods that operate at the Boolean level or use custom modifications, our automated behavioral synthesis method enables a wider range of possible approximations and can operate on arbitrary designs. Our method first creates an abstract synthesis tree (AST) from the input behavioral description, and then applies variant operators to the AST using an iterative stochastic greedy approach to identify the optimal inexact designs in an efficient way. Our method is able to identify the optimal designs that represent the Pareto frontier trade-off between accuracy and power consumption. Our methodology is developed into a tool we call ABACUS, which we integrate with a standard ASIC experimental flow based on industrial tools. We validate our methods on three realistic Verilog-based benchmarks from three different domains - signal processing, computer vision and machine learning. Our tool automatically discovers optimal designs, providing area and power savings of up to 50 while maintaining good accuracy.