. 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, computer-aided 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...

This paper extends the token flow model of Buck and Lee ([1],[2]), an analytical model for the behavior of dataflow graphs with data-dependent control flow, in two ways: dataflow actor execution may depend on integer, rather than Boolean, control tokens, and multiphase implementations of actors are permitted. These extensions permit data-dependent iteration to be modelled more naturally, reduce the memory required for implementations, and result in bounded-memory solutions in more cases than before. A method for generating efficient single-processor programs from the graphs is also described. 1. Introduction and

In this paper we address the problem of minimizing buffer storage requirement in constructing rate-optimal compile-time schedules for multi-rate dataflow graphs. We demonstrate that this problem, called the Minimum Buffer Rate-Optimal (MBRO) scheduling problem, can be formulated as a unified linear programming problem. A novel feature of our method is that it tries to minimize the memory requirement while simultaneously maximizing the computation rate. We have constructed an experimental testbed which implements our scheduling algorithm as well as (i) the widely used periodic admissible parallel schedules proposed by Lee and Messerschmitt [12], (ii) the optimal scheduling buffer allocation (OSBA) algorithm of Ning and Gao [15], and (iii) the multi-rate software pipelining (MRSP) algorithm [7]. The experimental results have demonstrated a significant improvement in buffer requirements for the MBRO schedules compared to the schedules generated by the other three methods. Compared to bloc...

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 time-critical 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 data-flow 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 intra-iteration and inter-iteration precedence relat...

Multimedia applications usually have throughput constraints. An implementation must meet these constraints, while it minimizes resource usage and energy consumption. The compute intensive kernels of these applications are often specified as Synchronous Dataflow Graphs. Communication between nodes in these graphs requires storage space which influences throughput. We present exact techniques to chart the Pareto space of throughput and storage tradeoffs, which can be used to determine the minimal storage space needed to execute a graph under a given throughput constraint. The feasibility of the approach is demonstrated with a number of examples.

The role of software is becoming increasingly important in the implementation of DSP applications. As this trend intensifies, and the complexity of applications escalates, we are seeing an increased need for automated tools to aid in the development of DSP software. This paper reviews the state of the art in programming language and compiler technology for DSP software implementation. In particular, we review techniques for high level, block-diagram-based modeling of DSP applications; the translation of block diagram specifications into efficient C programs using global, target-independent optimization techniques; and the compilation of C programs into streamlined machine code for programmable DSP processors, using architecture-specific and retargetable back-end optimizations. In our review, we also point out some important directions for further investigation.

This paper relates to system-level design of signal processing systems, which are often heterogeneous in implementation technologies and design styles. The heterogeneous approach, by combining small, specialized models of computation, achieves generality and also lends itself to automatic synthesis and formal verification. Key to the heterogeneous approach is to define interaction semantics that resolve the ambiguities when different models of computation are brought together. For this purpose, we introduce a tagged signal model as a formal framework within which the models of computation can be precisely described and unambiguously differentiated, and their interactions can be understood. In this paper, we will focus on the interaction between dataflow models, which have partially ordered events, and discrete-event models, with their notion of time that usually defines a total order of events. A variety of interaction semantics, mainly in handling the different notions of time in the two models, are explored to illustrate the subtleties involved. An implementation based on the Ptolemy system from U.C. Berkeley is described and critiqued.

Large-grain synchronous dataflow graphs or multi-rate graphs have the distinct feature that the nodes of the dataflow graph fire at different rates. Such multi-rate large-grain dataflow graphs have been widely regarded as a powerful programming model for DSP applications. In this paper we propose a method to minimize buffer storage requirement in constructing rate-optimal compile-time (MBRO) schedules for multi-rate dataflow graphs. We demonstrate that the constraints to minimize buffer storage while executing at the optimal computation rate (i.e. the maximum possible computation rate without storage constraints) can be formulated as a unified linear programming problem in our framework. A novel feature of our method is that it tries to minimize the memory requirement while simultaneously maximizing the computation rate. We have constructed an experimental testbed which implements our MBRO scheduling algorithm as well as (i) the widely used periodic admissible parallel schedules (also ...

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This paper reviews and extends an analytical model for the behavior of dataflow graphs with data-dependent control flow. The number of tokens produced or consumed by each actor is given as a symbolic function of the Booleans in the system. Long-term averages can be analyzed to determine consistency of token flow rates. Short-term behavior can be analyzed to construct an annotated schedule, or a static schedule that annotates each firing of an actor with the Boolean conditions under which that firing occurs. Necessary and sufficient conditions for bounded-length schedules, as well as sufficient conditions for determining that a dataflow graph can be scheduled in bounded memory are given. Annotated schedules can be used to generate efficient implementations of the algorithms described by the dataflow graphs. 1. Introduction The principal strength of dataflow graphs is that they do not over-specify an algorithm by imposing unnecessary sequencing constraints between operators. Instead, th...