We use a standard tree-structure representation for each individual. The GP constructs new attributes out of the continuous (real-valued) attributes of the data set being mined. Each individual corresponds to a candidate new attribute. The terminal set consists of all the continuous attributes in the data being mined. The function set consists of four arithmetic operators (+, -, *, /) and two r...

This paper presents some recent works on hardware evaluation of functions. A method for the automatic generation of high-performance arithmetic operators based on polynomial approximations is described. It deals with the bit-level representation of the polynomial coefficients, the intermediate computations width, the approximation and the rounding errors. The generated operators are small, fast...

Two different characterizations of self-dual aggregation operators are available in the literature: one based on C(x, y) = x/(x + 1 − y) and one based on the arithmetic mean. In this contribution, we fit the existing approaches into a more general framework and characterize N -invariant aggregation operators, with N an involutive negator. Special attention is drawn to the equivalence classes th...

Let G be a reductive algebraic group over Q, and suppose that Γ ⊂ G(R) is an arithmetic subgroup defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in L2(Γ\G(R)), and in general to determine the traces of Hecke operators on these spaces. In this paper we give a conjectural formula for the traces of Hecke operator...

This paper discusses machine learning of grammars and compilers of programming languages from samples of translation from source programs into object codes. This work is an application of incremental learning of definite clause grammars (DCGs) and syntax directed translation schema (SDTS), which is implemented in the Synapse system. The main experimental result is that Synapse synthesized a set...

In the LEC system, we employ a learning-driven approach for solving combinational data-path equivalence checking problems. The data-path logic is specified using Boolean and word-level operators in VHDL/Verilog. The targeted application area are Cto-RTL equivalence checking problems found in an industrial setting. These are difficult because of the algebraic transformations done on the data-pat...

The set Set(n), generated by an arbitrary natural number n, was defined in [2] and some arithmetic functions, over its elements are introduced algebraic aspect. Here, the of two functions similar to modal type operators their basic properties studied.

This paper is devoted to GPU kernel optimization and performance analysis of three tensorproduct operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close-to-the-peak performance for these operators requires extensive optimization because of the operators’ properties: low arithmetic intensity, tiered structu...