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Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Rotation scheduling: A loop pipelining algorithm
 Dept. of Computer Science, Princeton University
, 1997
"... Abstract — We consider the resourceconstrained scheduling of loops with interiteration dependencies. A loop is modeled as a data flow graph (DFG), where edges are labeled with the number of iterations between dependencies. We design a novel and flexible technique, called rotation scheduling, for sc ..."
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Cited by 98 (50 self)
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Abstract — We consider the resourceconstrained scheduling of loops with interiteration dependencies. A loop is modeled as a data flow graph (DFG), where edges are labeled with the number of iterations between dependencies. We design a novel and flexible technique, called rotation scheduling, for scheduling cyclic DFG’s using loop pipelining. The rotation technique repeatedly transforms a schedule to a more compact schedule. We provide a theoretical basis for the operations based on retiming. We propose two heuristics to perform rotation scheduling and give experimental results showing that they have very good performance. Index Terms — Highlevel synthesis, loop pipelining, parallel compiler, retiming, scheduling.
PathBased Scheduling for Synthesis
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1991
"... In the context of synthesis, scheduling assigns operations to control steps. Operations are the atomic components used for describing behavior, for example, arithmetic and Boolean operations. They are ordered partially by data dependencies (dataflow graph) and by control constructs such as condit ..."
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Cited by 87 (0 self)
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In the context of synthesis, scheduling assigns operations to control steps. Operations are the atomic components used for describing behavior, for example, arithmetic and Boolean operations. They are ordered partially by data dependencies (dataflow graph) and by control constructs such as conditional branches and loops (controlflow graph). A control step usually corresponds to one state, one clock cycle, or one microprogram step. This paper presents a new, pathbased scheduling algorithm. It yields solutions with the minimum number of control steps, taking into account arbitrary constraints that limit the amount of operations in each control step. The result is a finite state machine that implements the control. Although the complexity of the algorithm is proportional to the number of paths in the controlflow graph, it is shown to be practical for large examples with thousands of nodes.
Methods for Evaluating and Covering the Design Space during Early Design Development
 Integration, the VLSI Journal
, 2003
"... This paper gives an overview of methods used for Design Space Exploration (DSE) at the system and microarchitecture levels. The DSE problem is considered to be two orthogonal issues: (I) How could a single design point be evaluated, (II) how could the design space be covered during the explorat ..."
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Cited by 65 (0 self)
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This paper gives an overview of methods used for Design Space Exploration (DSE) at the system and microarchitecture levels. The DSE problem is considered to be two orthogonal issues: (I) How could a single design point be evaluated, (II) how could the design space be covered during the exploration process? The latter question arises since an exhaustive exploration of the design space by evaluating every possible design point is usually prohibitive due to the sheer size of the design space. We therefore reveal tradeo#s linked to the choice of appropriate evaluation and coverage methods. The designer has to balance the following issues: the accuracy of the evaluation, the time it takes to evaluate one design point (including the implementation of the evaluation model), the precision/granularity of the design space coverage, and last but not least the possibilities for automating the exploration process. We also list common representations of the design space and compare current system and microarchitecture level design frameworks. This review thus eases the choice of a decent exploration policy by providing a comprehensive survey and classification of recent related work. It is focused on SystemonaChip designs, particularly those used for network processors. These systems are heterogeneous in nature using multiple computation, communication, memory, and peripheral resources.
The Extended Partitioning Problem: Hardware/Software Mapping, Scheduling, and Implementationbin Selection
 PROCEEDINGS OF THE 6TH INTERNATIONAL WORKSHOP ON RAPID SYSTEMS PROTOTYPING
, 1997
"... In systemlevel design, applications are represented as task graphs where tasks (called nodes) have moderate to large granularity and each node has several implementation options differing in area and execution time. We define the extended partitioning problem as the joint determination of the mappi ..."
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Cited by 46 (2 self)
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In systemlevel design, applications are represented as task graphs where tasks (called nodes) have moderate to large granularity and each node has several implementation options differing in area and execution time. We define the extended partitioning problem as the joint determination of the mapping (hardware or software), the implementation option (called implementation bin), as well as the schedule, for each node, so that the overall area allocated to nodes in hardware is minimum and a deadline constraint is met. This problem is considerably harder (and richer) than the traditional binary partitioning problem that determines just the best mapping and schedule. Both binary and extended partitioning problems are constrained optimization problems and are NPhard. We first present an efficient (O(N²)) heuristic, called GCLP, to solve the binary partitioning problem. The heuristic reduces the greediness associated with traditional listscheduling algorithms by formulating a global m...
Information Theoretic Measures for Power Analysis
, 1996
"... This paper considers the problem of estimating the power consumption at logic and register transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informati ..."
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Cited by 41 (9 self)
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This paper considers the problem of estimating the power consumption at logic and register transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informational energy averages. For control circuits and random logic, the output entropy (informational energy) per bit is calculated as a function of the input entropy (informational energy) per bit and an implementation dependent information scaling factor. For datapath circuits, the output entropy (informational energy) is calculated from the input entropy (informational energy) using a compositional technique which has linear complexity in terms of the circuit size. Finally, from these input and output value, the entropy (informational energy) per circuit line is calculated and used as an estimate for the average switching activity. The proposed switching activity estimation technique does not r...
Scheduling And Behavioral Transformations For Parallel Systems
, 1993
"... In a parallel system, either a VLSI architecture in hardware or a parallel program in software, the quality of the final design depends on the ability of a synthesis system to exploit the parallelism hidden in the input description of applications. Since iterative or recursive algorithms are usually ..."
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Cited by 39 (3 self)
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In a parallel system, either a VLSI architecture in hardware or a parallel program in software, the quality of the final design depends on the ability of a synthesis system to exploit the parallelism hidden in the input description of applications. Since iterative or recursive algorithms are usually the most timecritical parts of an application, the parallelism embedded in the repetitive pattern of an iterative algorithm needs to be explored. This thesis studies techniques and algorithms to expose the parallelism in an iterative algorithm so that the designer can find an implementation achieving a desired execution rate. In particular, the objective is to find an efficient schedule to be executed iteratively. A form of dataflow graphs is used to model the iterative part of an application, e.g. a digital signal filter or the while/for loop of a program. Nodes in the graph represent operations to be performed and edges represent both intraiteration and interiteration precedence relat...
Recent Developments in HighLevel Synthesis
 ACM Transactions on Design Automation of Electronic Systems
, 1997
"... ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, N ..."
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Cited by 32 (0 self)
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ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA, fax +1 (212) 8690481, or permissions@acm.org Recent Development in High Level Synthesis y YounLong Lin Department of Computer Science Tsing Hua University HsinChu, Taiwan 30043, R. O. C. Abstract We survey recent development in high level synthesis technology for VLSI design. The need for higher level design automation tools are first discussed. We then describe some basic techniques for various subtasks of high level synthesis. Techniques that have been proposed in the past few years (since 1994) for various subtasks of high level synthesis are surveyed. We also survey some new synthesis objectives including testability, power efficiency and reliability. Keywords: High ...
Fast and Extensive SystemLevel Memory Exploration for ATM
 10th International Symposium on System Synthesis (Isss97
, 1997
"... In this paper, our memory architecture exploration methodology and CAD techniques for network protocol applications are presented. Prototype tools have been implemented, and applied on part of an industrial ATM application to show how our novel approach can be used to easily and thoroughly explore t ..."
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Cited by 29 (7 self)
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In this paper, our memory architecture exploration methodology and CAD techniques for network protocol applications are presented. Prototype tools have been implemented, and applied on part of an industrial ATM application to show how our novel approach can be used to easily and thoroughly explore the memory organization search space at the systemlevel. An extended, novel method for signal to memory assignment is proposed which takes into account memory access conflict constraints. The number of conflicts is first optimized by our flowgraph balancing technique. Significant power and area savings were obtained by performing the exploration thoroughly at each of the degrees of freedom in the global search space.
An Improved Method for RTL Synthesis with TestabilityTradeoffs
 In Proc. Intn'l Conf. on ComputerAided Design
, 1993
"... A method for highlevel synthesis with testability is presented with the objective to generate selftestable RTL datapath structures. We base our approach on a new improved testability model that generates various testable design styles while reducing the circuit sequential depth from controllable t ..."
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Cited by 26 (4 self)
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A method for highlevel synthesis with testability is presented with the objective to generate selftestable RTL datapath structures. We base our approach on a new improved testability model that generates various testable design styles while reducing the circuit sequential depth from controllable to observable registers. We follow the allocation method with an automatic test point selection algorithm and with an interactive tradeo# scheme which trades design area and delay with test quality. The method has been implemented and design comparisons arereported.