PolyGLoT: A Polyhedral Loop Transformation Framework for a Graphical Dataflow Language

Polyhedral techniques for program transformation are now used in several proprietary and open source compilers. However, most of the research on polyhedral compilation has focused on imperative languages such as C, where the computation is specified in terms of statements with zero or more nested loops and other control structures around them. Graphical dataflow languages, where there is no notion of statements or a schedule specifying their relative execution order, have so far not been studied using a powerful transformation or optimization approach. The execution semantics and referential transparency of dataflow languages impose a different set of challenges. In this paper, we attempt to bridge this gap by presenting techniques that can be used to extract polyhedral representation from dataflow programs and to synthesize them from their equivalent polyhedral representation. We then describe PolyGLoT, a framework for automatic transformation of dataflow programs which we built using our techniques and other popular research tools such as Clan and Pluto. For the purpose of experimental evaluation, we used our tools to compile LabVIEW, one of the most widely used dataflow programming languages. Results show that dataflow programs transformed using our framework are able to outperform those compiled otherwise by up to a factor of seventeen, with a mean speed-up of 2.30x while running on an 8-core Intel system.

Space and time efficiency of the forest-of-quadtrees representation

A forest of quadtrees is a refinement of a quadtree data structure that is used to represent planar regions. A forest of quadtrees provides space savings over regular quadtrees by concentrating vital information. The paper presents some of the properties of a forest of quadtrees and studies the storage requirements for the case in which a single 2m × 2m region is equally likely to occur in any position within a 2n × 2n image. Space and time efficiency are investigated for the forest-of-quadtrees representation as compared with the quadtree representation for various cases.

Generalized Query-By-Rule: a heterogeneous database query language

This paper describes the design and implementation of a high-level query language called Generalized Query-By-Rule (GQBR) which supports retrieval, insertion, deletion and update operations. This language, based on the formalism of database logic, enables the users to access each database in a distributed heterogeneous environment, without having to learn all the different data manipulation languages. The compiler has been implemented on a DEC 1090 system in Pascal.

Access path query language for relational database systems

Database management systems offer a very reliable and attractive data organization for fast and economical information storage and processing for diverse applications. It is much more important that the information should be easily accessible to users with varied backgrounds, professional as well as casual, through a suitable data sublanguage. The language adopted here (APPLE) is one such language for relational database systems and is completely nonprocedural and well suited to users with minimum or no programming background. This is supported by an access path model which permits the user to formulate completely nonprocedural queries expressed solely in terms of attribute names. The data description language (DDL) and data manipulation language (DML) features of APPLE are also discussed. The underlying relational database has been implemented with the help of the DATATRIEVE-11 utility for record and domain definition which is available on the PDP-11/35. The package is coded in Pascal and MACRO-11. Further, most of the limitations of the DATATRIEVE-11 utility have been eliminated in the interface package.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Linear time geometrical design rule checker based on quadtree representation of VLSI mask layouts

An efficient geometrical design rule checker is proposed, based on operations on quadtrees, which represent VLSI mask layouts. The time complexity of the design rule checker is O(N), where N is the number of polygons in the mask. A pseudoPascal description is provided of all the important algorithms for geometrical design rule verification.

Reflexive Incidence Matrx (RIM) Representation of Petr Nets

Although incidence matrix representation has been used to analyze the Petri net based models of a system, it has the limitation that it does not preserve reflexive properties (i.e., the presence of selfloops) of Petri nets. But in many practical applications self-loops play very important roles. This paper proposes a new representation scheme for general Petri nets. This scheme defines a matrix called "reflexive incidence matrix (RIM) c which is a combination of two matrices, a "base matrix Cb,,, and a "power matrix CP." This scheme preserves the reflexive and other properties of the Petri nets. Through a detailed analysis it is shown that the proposed scheme requires less memory space and less processing time for answering commonly encountered net queries compared to other schemes. Algorithms to generate the RIM from the given net description and to decompose RIM into input and output function matrices are also given. The proposed Petri net representation scheme is very useful to model and analyze the systems having shared resources, chemical processes, network protocols, etc., and to evaluate the performance of asynchronous concurrent systems.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

A new formalism for representation of binary thermodynamic data

The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.

An interpreter for slips-An applicative language based on LAMBDA-Calculus

An applicative language based on the LAMBDA-Calculus is presented. The language, SLIPS (Small Language for Instruction Purposes), is described using the LAMBDA-Calculus as a metalanguage. A call-by-need mechanism of function invocation eliminates the drawbacks of both call-by-name and call-by-value. The system has been implemented in PASCAL.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

DFL: A Data Flow Language

Many novel computer architectures like array and multiprocessors which achieve high performance through the use of concurrency exploit variations of the von Neumann model of computation. The effective utilization of the machines makes special demands on programmers and their programming languages, such as the structuring of data into vectors or the partitioning of programs into concurrent processes. In comparison, the data flow model of computation demands only that the principle of structured programming be followed. A data flow program, often represented as a data flow graph, is a program that expresses a computation by indicating the data dependencies among operators. A data flow computer is a machine designed to take advantage of concurrency in data flow graphs by executing data independent operations in parallel. In this paper, we discuss the design of a high level language (DFL: Data Flow Language) suitable for data flow computers. Some sample procedures in DFL are presented. The implementation aspects have not been discussed in detail since there are no new problems encountered. The language DFL embodies the concepts of functional programming, but in appearance closely resembles Pascal. The language is a better vehicle than the data flow graph for expressing a parallel algorithm. The compiler has been implemented on a DEC 1090 system in Pascal.

Representation of Stereoisomers in ALWIN

Tlhe well-known Cahn-lngold-Prelog method of specifying the stereoisomers is introduced within the framework of ALWIN-Algorithmic Wiswesser Notation. Given the structural diagram, the structural ALWIN is first formed; the speclflcation symbols are then introduced at the appropriate places to describe the stereoisomers.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Geometric Representation of Graphs in Low Dimension Using Axis Parallel Boxes

An axis-parallel k-dimensional box is a Cartesian product R-1 x R-2 x...x R-k where R-i (for 1 <= i <= k) is a closed interval of the form [a(i), b(i)] on the real line. For a graph G, its boxicity box(G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds applications in various areas such as ecology, operations research etc. A number of NP-hard problems are either polynomial time solvable or have much better approximation ratio on low boxicity graphs. For example, the max-clique problem is polynomial time solvable on bounded boxicity graphs and the maximum independent set problem for boxicity d graphs, given a box representation, has a left perpendicular1 + 1/c log n right perpendicular(d-1) approximation ratio for any constant c >= 1 when d >= 2. In most cases, the first step usually is computing a low dimensional box representation of the given graph. Deciding whether the boxicity of a graph is at most 2 itself is NP-hard. We give an efficient randomized algorithm to construct a box representation of any graph G on n vertices in left perpendicular(Delta + 2) ln nright perpendicular dimensions, where Delta is the maximum degree of G. This algorithm implies that box(G) <= left perpendicular(Delta + 2) ln nright perpendicular for any graph G. Our bound is tight up to a factor of ln n. We also show that our randomized algorithm can be derandomized to get a polynomial time deterministic algorithm. Though our general upper bound is in terms of maximum degree Delta, we show that for almost all graphs on n vertices, their boxicity is O(d(av) ln n) where d(av) is the average degree.