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187
Automatic Translation of FORTRAN Programs to Vector Form
 ACM Transactions on Programming Languages and Systems
, 1987
"... This paper discusses the theoretical concepts underlying a project at Rice University to develop an automatic translator, called PFC (for Parallel FORTRAN Converter), from FORTRAN to FORTRAN 8x. The Rice project, based initially upon the research of Kuck and others at the University of Illinois [6, ..."
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Cited by 324 (34 self)
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This paper discusses the theoretical concepts underlying a project at Rice University to develop an automatic translator, called PFC (for Parallel FORTRAN Converter), from FORTRAN to FORTRAN 8x. The Rice project, based initially upon the research of Kuck and others at the University of Illinois [6, 1721, 24, 32, 36], is a continuation of work begun while on leave at IBM Research in Yorktown Heights, N.Y. Our first implementation was based on the Illinois PARAFRASE compiler [20, 36], but the current version is a completely new program (although it performs many of the same transformations as PARAFRASE). Other projects that have influenced our work are the Texas Instruments ASC compiler [9, 33], the Cray1 FORTRAN compiler [15], and the Massachusetts Computer Associates Vectorizer [22, 25]. The paper is organized into seven sections. Section 2 introduces FORTRAN 8x and gives examples of its use. Section 3 presents an overview of the translation process along with an extended translation example. Section 4 develops the concept of interstatement dependence and shows how it can be applied to the problem of vectorization. Loop carried dependence and loop independent dependence are introduced in this section to extend dependence to multiple statements and multiple loops. Section 5 develops dependencebased algorithms for code generation and transformations for enhancing the parallelism of a statement. Section 6 describes a method for extending the power of data dependence to control statements by the process of IF conversion. Finally, Section 7 details the current state of PFC and our plans for its continued development
Efficient Büchi Automata from LTL Formulae
 CAV 2000, LNCS 1855:247–263
, 2000
"... We present an algorithm to generate small Büchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal w ..."
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Cited by 121 (13 self)
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We present an algorithm to generate small Büchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting setspossibly reducing the strength of the resulting automaton. This leads to more efficient model checking of lineartime logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.
Mini: A heuristic approach for logic minimization
 IBM Journal of Research and Development
, 1974
"... Abstract: MINI is a heuristic logic minimization technique for manyvariable problems. It accepts as input a Boolean logic specification expressed as an inputoutput table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which ca ..."
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Cited by 61 (0 self)
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Abstract: MINI is a heuristic logic minimization technique for manyvariable problems. It accepts as input a Boolean logic specification expressed as an inputoutput table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which can be converted to prime implicants if desired. New and effective subprocesses, such as expanding, reshaping, and removing redundancy from cubes, are iterated until there is no further reduction in the solution. The process is general in that it can minimize both conventional logic and logic functions of multivalued variables.
The Minimum Equivalent DNF Problem and Shortest Implicants
, 1998
"... We prove that the Minimum Equivalent DNF problem is \Sigma p 2 complete, resolving a conjecture due to Stockmeyer. The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain ..."
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Cited by 51 (4 self)
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We prove that the Minimum Equivalent DNF problem is \Sigma p 2 complete, resolving a conjecture due to Stockmeyer. The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain certain results concerning the complexity of the Shortest Implicant problem that may be of independent interest. When the input is a formula, the Shortest Implicant problem is \Sigma p 2  complete, and \Sigma p 2 hard to approximate to within an n 1=2\Gammaffl factor. When the input is a circuit, approximation is \Sigma p 2  hard to within an n 1\Gammaffl factor. However, when the input is a DNF formula, the Shortest Implicant problem cannot be \Sigma p 2 complete unless \Sigma p 2 = NP[log 2 n] NP . 1. Introduction Twolevel (DNF) logic minimization is a central practical problem in logic synthesis and also one of the more natural problems in the polynomial hierarchy....
A Continuous Approach to Inductive Inference
 Mathematical Programming
, 1992
"... In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g ..."
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Cited by 43 (2 self)
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In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g using outputs obtained by applying a limited number of random inputs to the hidden function. Given this inputoutput sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used...
Exact and heuristic algorithms for the minimization of incompletely specified state machines
 IEEE Transactions on ComputerAided Design
, 1994
"... AbstractIn this paper we present two exact algorithms for state minimization of FSM’s. Our results prove that exact state minimization is feasible for a large class of practical examples, certainly including most handdesigned FSM’s. We also present heuristic algorithms, that can handle large, mach ..."
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Cited by 42 (0 self)
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AbstractIn this paper we present two exact algorithms for state minimization of FSM’s. Our results prove that exact state minimization is feasible for a large class of practical examples, certainly including most handdesigned FSM’s. We also present heuristic algorithms, that can handle large, machinegenerated, FSM’s. The possibly many different reduced machines with the same number of states have different implementation costs. We discuss two steps of the minimization procedure, called state mapping and solution shrinking, that have received little prior attention in the literature, though they play a significant role in delivering an optimally implemented reduced machine. We also introduce an algorithm whose main virtue is the ability to cope with very general cost functions, while providing high performance. I.
Exploiting lineage for confidence computation in uncertain and probabilistic databases
, 2007
"... We study the problem of computing query results with confidence values in ULDBs: relational databases with uncertainty and lineage. ULDBs, which subsume probabilistic databases, offer an alternative decoupled method of computing confidence values: Instead of computing confidences during query proc ..."
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Cited by 40 (10 self)
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We study the problem of computing query results with confidence values in ULDBs: relational databases with uncertainty and lineage. ULDBs, which subsume probabilistic databases, offer an alternative decoupled method of computing confidence values: Instead of computing confidences during query processing, compute them afterwards based on lineage. This approach enables a wider space of query plans, and it permits selective computations when not all confidence values are needed. This paper develops a suite of algorithms and optimizations for a broad class of relational queries on ULDBs. We provide confidence computation algorithms for single data items, as well as efficient batch algorithms to compute confidences for an entire relation or database. All algorithms incorporate memoization to avoid redundant computations, and they have been implemented in the Trio prototype ULDB database system. Performance characteristics and scalability of the algorithms are demonstrated through experimental results over a large synthetic dataset. 1.
ESPRESSOSIGNATURE: A New Exact Minimizer for Logic Functions
 Proc. DAC ’93
, 1996
"... We present a new algorithm for exact twolevel logic optimization. We represent a set of primes by the cube of their intersection. Therefore, the unique set of sets of primes which forms the covering problem can be implicitly represented by a set of cubeswhich forms a minimum canonical cover. We obt ..."
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Cited by 38 (1 self)
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We present a new algorithm for exact twolevel logic optimization. We represent a set of primes by the cube of their intersection. Therefore, the unique set of sets of primes which forms the covering problem can be implicitly represented by a set of cubeswhich forms a minimum canonical cover. We obtain the minimum canonical cover starting from any initial cover and then derive the table covering problem. The method is effective; it improves on the runtime and memory usage of ESPRESSOEXACT by average factors of 1.78 and 1.2x respectively on the 114 of 134 benchmark examples that could be completed by ESPRESSOEXACT. Of the remaining 20 hard problems, we solve 14 exactly. For 3 of the remaining 6 we derive the covering table but the covering problem could not be solved exactly. The remaining 3 remains intractable for the moment. This research supported by Fujitsu Research y Department of Electrical Engineering and Computer Sciences, University of California Berkeley 1 Introduction...
Solving Covering Problems Using LPRBased Lower Bounds
 In Proceedings of the ACM/IEEE Design Automation Conference
, 1996
"... Unate and binate covering problems are a special class of general integer linear programming problems with which several problems in logic synthesis, such as twolevel logic minimization and technology mapping, are formulated. Previous branchandbound methods for exactly solving these problems use ..."
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Cited by 38 (1 self)
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Unate and binate covering problems are a special class of general integer linear programming problems with which several problems in logic synthesis, such as twolevel logic minimization and technology mapping, are formulated. Previous branchandbound methods for exactly solving these problems use lowerbounding techniques based on finding maximal independent sets. In this paper we examine lowerbounding techniques based on linear programming relaxation (LPR) for the binate covering problem. We show that a combination of traditional reductions (essentiality and dominance) and incremental computation of LPRbased lower bounds can exactly solve difficult covering problems orders of magnitude faster than traditional methods. KeywordsCovering problems, integer linear programming I. INTRODUCTION Covering problems (unate and binate) are important combinatorial optimization problems with which several problems in logic synthesis (such as twolevel logic minimization [12], state minimizati...
SOCRATES: A system for automatically synthesizing and optimizing combinational logic
 in 23rd Design Automation Conference
, 1986
"... This paper presents SOCRATES, a system of programs which Synthesize and optimize combinational logic circuits, from boolean equations. SOCRATES optimizes logic using boolean and algebraic minimization techniques, and it optimizes circuits derived from this logic in a user defined technology with a ..."
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Cited by 31 (1 self)
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This paper presents SOCRATES, a system of programs which Synthesize and optimize combinational logic circuits, from boolean equations. SOCRATES optimizes logic using boolean and algebraic minimization techniques, and it optimizes circuits derived from this logic in a user defined technology with a rule based expert system. This paper discusses the goals of logic synthesis and the capabilities needed in a tool to meet these goals. SOCRATES’s capabilities are then presented and demonstrated with experiments run on circuits from the 1986 Design Automation Conference synthesis benchmark set.