On the Complexity of Optimization Problems based on Compiled NNF Representations

Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard. Fortunately, in many problems, the set of feasible solutions does not often change and is independent from the user's request. In such cases, compiling the set of constraints describing the set of feasible solutions during an off-line phase makes sense, if this compilation step renders computationally easier the generation of a non-dominated, yet feasible solution matching the user's requirements and preferences (which are only known at the on-line step). In this article, we focus on propositional constraints. The subsets L of the NNF language analyzed in Darwiche and Marquis' knowledge compilation map are considered. A number of families F of representations of objective functions over propositional variables, including linear pseudo-Boolean functions and more sophisticated ones, are considered. For each language L and each family F, the complexity of generating an optimal solution when the constraints are compiled into L and optimality is to be considered w.r.t. a function from F is identified

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

LOT: Logic Optimization with Testability - new transformations for logic synthesis

A new approach to optimize multilevel logic circuits is introduced. Given a multilevel circuit, the synthesis method optimizes its area while simultaneously enhancing its random pattern testability. The method is based on structural transformations at the gate level. New transformations involving EX-OR gates as well as Reed–Muller expansions have been introduced in the synthesis of multilevel circuits. This method is augmented with transformations that specifically enhance random-pattern testability while reducing the area. Testability enhancement is an integral part of our synthesis methodology. Experimental results show that the proposed methodology not only can achieve lower area than other similar tools, but that it achieves better testability compared to available testability enhancement tools such as tstfx. Specifically for ISCAS-85 benchmark circuits, it was observed that EX-OR gate-based transformations successfully contributed toward generating smaller circuits compared to other state-of-the-art logic optimization tools

Recent advances in the theory and practice of logical analysis of data

Logical Analysis of Data (LAD) is a data analysis methodology introduced by Peter L. Hammer in 1986. LAD distinguishes itself from other classification and machine learning methods by the fact that it analyzes a significant subset of combinations of variables to describe the positive or negative nature of an observation and uses combinatorial techniques to extract models defined in terms of patterns. In recent years, the methodology has tremendously advanced through numerous theoretical developments and practical applications. In the present paper, we review the methodology and its recent advances, describe novel applications in engineering, finance, health care, and algorithmic techniques for some stochastic optimization problems, and provide a comparative description of LAD with well-known classification methods

Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

Multi-Quality Auto-Tuning by Contract Negotiation

A characteristic challenge of software development is the management of omnipresent change. Classically, this constant change is driven by customers changing their requirements. The wish to optimally leverage available resources opens another source of change: the software systems environment. Software is tailored to specific platforms (e.g., hardware architectures) resulting in many variants of the same software optimized for different environments. If the environment changes, a different variant is to be used, i.e., the system has to reconfigure to the variant optimized for the arisen situation. The automation of such adjustments is subject to the research community of self-adaptive systems. The basic principle is a control loop, as known from control theory. The system (and environment) is continuously monitored, the collected data is analyzed and decisions for or against a reconfiguration are computed and realized. Central problems in this field, which are addressed in this thesis, are the management of interdependencies between non-functional properties of the system, the handling of multiple criteria subject to decision making and the scalability. In this thesis, a novel approach to self-adaptive software--Multi-Quality Auto-Tuning (MQuAT)--is presented, which provides design and operation principles for software systems which automatically provide the best possible utility to the user while producing the least possible cost. For this purpose, a component model has been developed, enabling the software developer to design and implement self-optimizing software systems in a model-driven way. This component model allows for the specification of the structure as well as the behavior of the system and is capable of covering the runtime state of the system. The notion of quality contracts is utilized to cover the non-functional behavior and, especially, the dependencies between non-functional properties of the system. At runtime the component model covers the runtime state of the system. This runtime model is used in combination with the contracts to generate optimization problems in different formalisms (Integer Linear Programming (ILP), Pseudo-Boolean Optimization (PBO), Ant Colony Optimization (ACO) and Multi-Objective Integer Linear Programming (MOILP)). Standard solvers are applied to derive solutions to these problems, which represent reconfiguration decisions, if the identified configuration differs from the current. Each approach is empirically evaluated in terms of its scalability showing the feasibility of all approaches, except for ACO, the superiority of ILP over PBO and the limits of all approaches: 100 component types for ILP, 30 for PBO, 10 for ACO and 30 for 2-objective MOILP. In presence of more than two objective functions the MOILP approach is shown to be infeasible