Function extraction

AbstractLow-level imperative programming languages typically have complex operational semantics (e.g. derived from an underlying processor architecture). In this paper, we describe an automatic method for extracting recursive functions from such low-level programs. The functions are derived by formal deduction from the semantics of the programming language. For each function extracted, a proof of correspondence to the original program is automatically constructed. Subsequent program verification can then be done without referring to the details of the low-level programming language semantics at all: it suffices to prove properties of the extracted function. The technique is explained for simple while programs and also for the machine code of a widely used processor. We show how heuristics can enhance the output from the function extractor/decompiler and how the technique aids implementation of a trustworthy compiler. Our tools have been implemented in the HOL4 theorem prover

Jet reconstruction in heavy ion collisions (emphasis on Underlying Event background subtraction)

A modification of the internal structure of jets is expected due to the production of a dense QCD medium, the Quark Gluon Plasma, in heavy-ion collisions. We discuss some aspects of jet reconstruction in p+p and A+A collisions and emphasize the dramatically increased contribution of the underlying event in nucleus-nucleus collisions as compared with the vacuum case. We conclude with its consequences on the full jet spectrum and fragmentation function extraction at LHC.Comment: 10 pages, talk given at First International Workshop on Multiple Partonic Interactions at the LHC, "MPI@LHC'08", Perugia, Italy, October 27-31 200

Nucleon Structure Functions and Nuclear DIS

The nucleon structure study in nuclear deep inelastic scattering is considered. It is shown that nuclear data provide a new source of information about dynamics of parton distributions in the nucleon. An example of the neutron structure function extraction from the deuteron and proton data is considered. The limit $x\to 1$ of the neutron to proton structure functions ratio is studied. A link between the deep inelastic scattering off the nucleon at high $x$ and elastic scattering off nuclei in high $Q^2$ region is discussed.Comment: 4 pages, 5 figures, Contributed to the Proceedings of the HiX2004 Workshop, 26-28 July 2004, Marseill

Cancellation of Spurious Arrivals in Green’s Function Extraction

The extraction of the Green\u27s function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green\u27s function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium

Formal Verification of Arithmetic Circuits by Function Extraction

The paper presents an algebraic approach to functional verification of gate-level, integer arithmetic circuits. It is based on extracting a unique bit-level polynomial function computed by the circuit directly from its gate-level implementation. The method can be used to verify the arithmetic function computed by the circuit against its known specification, or to extract an arithmetic function implemented by the circuit. Experiments were performed on arithmetic circuits synthesized and mapped onto standard cells using ABC system. The results demonstrate scalability of the method to large arithmetic circuits, such as multipliers, multiply-accumulate, and other elements of arithmetic datapaths with up to 512-bit operands and over 2 million gates. The results show that our approach wins over the state-of-the-art SAT/SMT solvers by several orders of magnitude of CPU time. The procedure has linear runtime and memory complexity, measured by the number of logic gates

First extraction of Interference Fragmentation Functions from e+e- data

We report on the first extraction of interference fragmentation functions from the semi-inclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite \pi+\pi- pairs is related to the transverse polarization of fragmenting quarks through a significant polarized dihadron fragmentation function. Extraction of the latter requires the knowledge of its unpolarized counterpart, the probability density for a quark to fragment in a \pi+\pi- pair. Since data for the unpolarized cross section are missing, we extract the unpolarized dihadron fragmentation function from a Monte Carlo simulation of the cross section.Comment: 17 pages, 7 (multiple) figures, 15 tables, RevTeX format; refined version of the fit, conclusions unchanged; added referenc

Elite Bases Regression: A Real-time Algorithm for Symbolic Regression

Symbolic regression is an important but challenging research topic in data mining. It can detect the underlying mathematical models. Genetic programming (GP) is one of the most popular methods for symbolic regression. However, its convergence speed might be too slow for large scale problems with a large number of variables. This drawback has become a bottleneck in practical applications. In this paper, a new non-evolutionary real-time algorithm for symbolic regression, Elite Bases Regression (EBR), is proposed. EBR generates a set of candidate basis functions coded with parse-matrix in specific mapping rules. Meanwhile, a certain number of elite bases are preserved and updated iteratively according to the correlation coefficients with respect to the target model. The regression model is then spanned by the elite bases. A comparative study between EBR and a recent proposed machine learning method for symbolic regression, Fast Function eXtraction (FFX), are conducted. Numerical results indicate that EBR can solve symbolic regression problems more effectively.Comment: The 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2017

Symbolic Regression with Fast Function Extraction and Nonlinear Least Squares Optimization

Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite.Comment: Submitted manuscript to be published in Computer Aided Systems Theory - EUROCAST 2022: 18th International Conference, Las Palmas de Gran Canaria, Feb. 202