Abstract — Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performance-critical domain of linear digital signal processing (DSP) transforms. For a specified transform, SPIRAL automatically generates high performance code that is tuned to the given platform. SPIRAL formulates the tuning as an optimization problem, and exploits the domain-specific mathematical structure of transform algorithms to implement a feedback-driven optimizer. Similar to a human expert, for a specified transform, SPIRAL “intelligently ” generates and explores algorithmic and implementation choices to find the best match to the computer’s microarchitecture. The “intelligence” is provided by search and learning techniques that exploit the structure of the algorithm and implementation space to guide the exploration and optimization. SPIRAL generates high performance code for a broad set of DSP transforms including the discrete Fourier transform, other trigonometric transforms, filter transforms, and discrete wavelet transforms. Experimental results show that the code generated by SPIRAL competes with, and sometimes outperforms, the best available human tuned transform library code. Index Terms — library generation, code optimization, adaptation, automatic performance tuning, high performance computing, linear signal transform, discrete Fourier transform, FFT, discrete cosine transform, wavelet, filter, search, learning, genetic and evolutionary algorithm, Markov decision process I.

SPIRAL is a generator for libraries of fast software implementations of linear signal processing transforms. These libraries are adapted to the computing platform and can be re-optimized as the hardware is upgraded or replaced. This paper describes the main components of SPIRAL: the mathematical framework that concisely describes signal transforms and their fast algorithms; the formula generator that captures at the algorithmic level the degrees of freedom in expressing a particular signal processing transform; the formula translator that encapsulates the compilation degrees of freedom when translating a specific algorithm into an actual code implementation; and, finally, an intelligent search engine that finds within the large space of alternative formulas and implementations

Evolution of symbolic language and grammar is studied in a network model. Language is expressed by words, i.e. strings of symbols, which are generated by agents with their own symbolic grammar system. Agents communicate with each other by deriving and accepting words in terms of their own grammar. They are ranked according to their communicative effectiveness: an agent which can derive less frequent and less acceptable words and accept words in less computational time will have higher scores. They can evolve by mutational processes, which change rewriting rules in their symbolic grammars. Complexity and diversity of words increase in the course of time. The emergence of modules and loop structure enhances the evolution. On the other hand, ensemble structure lead to a net-grammar, restricting individual grammars and their evolution. Key words: Net-grammar; Algorithmic evolution; Module-type evolution; Evolution of language; Symbolic grammar systems 1 Introduction Linguistic expressions...

In a graphical user interface, physical layout and abstract structure are two important aspects of a graph. This article proposes a new graph grammar formalism which integrates both the spatial and structural specification mechanisms in a single framework. This formalism is equipped with a parser that performs in polynomial time with an improved parsing complexity over its nonspatial predecessor, that is, the Reserved Graph Grammar. With the extended expressive power, the formalism is suitable for many user interface applications. The article presents its application in adaptive Web design and presentation.

Abstract. Evolution of symbolic language and grammar is studied in a network model. Language is expressed by words, i.e. strings of symbols, which are generated by agents with their own symbolic grammar system. By deriving and accepting words, the agents communicate with each other. An agent which can derive less frequent and less acceptable words and accept words in less computational time will have higher scores. Grammars of agents can evolve bymutationally processes, where higher scored agents have more chances to breed their o springs with improved grammar system. Complexity and diversity ofwords increase in time. It is found that the module type evolution and the emergence of loop structure enhance the evolution. Furthermore, ensemble structure (net-grammar) emerges from interaction among individual grammar systems. A net-grammar restricts structures of individual grammar and determines their evolutionary pathway. 1

Given > 1, an expansion of x 2 [0; 1) base is the encoding of the transformation T (x) = x (mod 1) into the space f0; : : : ; [ ]g where [ ] is the integer part of . The beta-shift is the closure of the set of beta-expansions of points in [0; 1). There is also a lexicographic description of the beta-shift, as well as the expansion of 1 base , which completely determines membership in the beta-shift. This

In the quest for a useful syntax for language definition formalisms --- the SDF part of ASD+SDF of Klint and his co-workers --- Visser has proposed to extend context free rules with reject productions. We propose to modify the definition to ensure modularity of reject grammars. Next, attention is drawn to the close link between reject grammars (under the modified definition), indexed least fixpoint grammars (Rounds) and simple literal movement grammars (Groenink). This link indicates that reject grammars are closely related to the `mildly context-sensitive' grammar formalisms that have been developed for use in natural language analysis. 1 Reject Grammars To increase the versatility of the ASD+SDF meta-environment for specification and syntax definition created by Paul Klint and his co-workers [6], Visser [9] proposes to add reject rules A ! r A 1 \Delta \Delta \Delta An to CF grammars. The recipe for handling these reject rules is, roughly, the following: if A ! r ff is a rule of the...

In this paper, we present first a brief survey of some techniques in regular grammar inference. The core of the discussion is then to try to classify these different methods within a unique framework. A first step in that direction [10] has introduced a general methodology based on letter-to-letter morphisms. We pursue that work and propose successively paradigms based on rewriting morphisms, substitutions, and transductions.

The paper describes design of the FLUTE system, an intelligent tutoring system in the domain of formal languages and automata. The basic idea of the FLUTE system is a systematic introduction of students into the system's domain, in accordance with both the logical structure of the domain and individual background knowledge and learning capabilities of each student. Other intelligent tutoring systems in that domain are not described in the open literature. The knowledge in the FLUTE system is represented starting from ITS ontology that has been defined within a recently developed framework and a model of intelligent tutoring systems, called GET-BITS. A brief overview of the model/framework is also included. The contents that should be presented to the student during tutoring sessions are discussed and logical organization of such contents within the system is described. The system is analyzed in the paper from the pedagogical point of view. Every concept that a student has to l...

Grammar inference is the learning or model estimation required by any syntatic approach to pattern recognition. Given a sample of strings, the grammar inference procedure must infer the grammar which has generated these strings. Decidability questions have been discussed by Gold and they depend largely on the availability of all positive samples (known to have been generated by the grammar) and negative samples (strings not generated by the grammar). Restrictions on the grammar inference problem may apply: one may either constrain the set of positive samples or the set of negative samples, or the class of grammars where the solution has to be looked for, or even the complexity of the grammar inference procedure.