Invariant Generation for Multi-Path Loops with Polynomial Assignments

Program analysis requires the generation of program properties expressing conditions to hold at intermediate program locations. When it comes to programs with loops, these properties are typically expressed as loop invariants. In this paper we study a class of multi-path program loops with numeric variables, in particular nested loops with conditionals, where assignments to program variables are polynomial expressions over program variables. We call this class of loops extended P-solvable and introduce an algorithm for generating all polynomial invariants of such loops. By an iterative procedure employing Gr\"obner basis computation, our approach computes the polynomial ideal of the polynomial invariants of each program path and combines these ideals sequentially until a fixed point is reached. This fixed point represents the polynomial ideal of all polynomial invariants of the given extended P-solvable loop. We prove termination of our method and show that the maximal number of iterations for reaching the fixed point depends linearly on the number of program variables and the number of inner loops. In particular, for a loop with m program variables and r conditional branches we prove an upper bound of m*r iterations. We implemented our approach in the Aligator software package. Furthermore, we evaluated it on 18 programs with polynomial arithmetic and compared it to existing methods in invariant generation. The results show the efficiency of our approach

Peep Show

An Army veteran reaches out to protect the younger generation when a teen wanders into an adult video shop. Articles, stories, and other compositions in this archive were written by participants in the Mighty Pen Project. The program, developed by author David L. Robbins, and in partnership with Virginia Commonwealth University and the Virginia War Memorial in Richmond, Virginia, offers veterans and their family members a customized twelve-week writing class, free of charge. The program encourages, supports, and assists participants in sharing their stories and experiences of military experience so both writer and audience may benefit

Automated mass spectrum generation for new physics

We describe an extension of the FeynRules package dedicated to the automatic generation of the mass spectrum associated with any Lagrangian-based quantum field theory. After introducing a simplified way to implement particle mixings, we present a new class of FeynRules functions allowing both for the analytical computation of all the model mass matrices and for the generation of a C++ package, dubbed ASperGe. This program can then be further employed for a numerical evaluation of the rotation matrices necessary to diagonalize the field basis. We illustrate these features in the context of the Two-Higgs-Doublet Model, the Minimal Left-Right Symmetric Standard Model and the Minimal Supersymmetric Standard Model.Comment: 11 pages, 1 table; version accepted by EPJ

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small

Lagrangian Theory of Constrained Systems: Cosmological Application

Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a second-class primary constraint linear in the momenta and a second-class secondary constraint quadratic in the momenta. This paper studies in detail the same problem at a Lagrangian level, i.e. working on the tangent bundle rather than on phase space. The corresponding analysis is motivated by a more general program, aiming to obtain a manifestly covariant, multisymplectic framework for the analysis of relativistic theories of gravitation regarded as constrained systems. After an application of the Gotay-Nester Lagrangian analysis, the paper deals with the generalized method, which has the advantage of being applicable to any system of differential equations in implicit form. Multiplication of the second-order Lagrange equations by a vector with zero eigenvalue for the Hessian matrix yields the so-called first-generation constraints. Remarkably, in the cosmological model here considered, if Lagrange equations are studied using second-order formalism, a second-generation constraint is found which is absent in first-order formalism. This happens since first- and second-order formalisms are inequivalent. There are, however, no {\it a priori} reasons for arguing that one of the two is incorrect. First- and second-generation constraints are used to derive physical predictions for the cosmological model.Comment: 22 pages, plain-tex, recently appearing in Nuovo Cimento B, volume 109, pages 1259-1273, December 199

Deriving The Standard Model From Superstring Theory

I outline a program to derive the Standard Model directly from superstring theory. I present a class of three generation superstring standard--like models in the free fermionic formulation. I discuss some phenomenological properties of these models. In particular these models suggest an explanation for the top quark mass hierarchy. A numerical estimate yielded $m_t\sim175-180~GeV$. The general texture of fermion mass matrices was obtained from analysis of nonrenormalizable terms up to order $N=8$.I argue that the realistic features of these models are due to the underlying $Z_2\times Z_2$ orbifold, with standard embedding, at the free fermionic point in toroidal compactification space.Comment: IASSNS--HEP--94/21, 11 page

Affine Disjunctive Invariant Generation with Farkas' Lemma

Invariant generation is the classical problem that aims at automated generation of assertions that over-approximates the set of reachable program states in a program. We consider the problem of generating affine invariants over affine while loops (i.e., loops with affine loop guards, conditional branches and assignment statements), and explore the automated generation of disjunctive affine invariants. Disjunctive invariants are an important class of invariants that capture disjunctive features in programs such as multiple phases, transitions between different modes, etc., and are typically more precise than conjunctive invariants over programs with these features. To generate tight affine invariants, existing constraint-solving approaches have investigated the application of Farkas' Lemma to conjunctive affine invariant generation, but none of them considers disjunctive affine invariants

Program Termination and Worst Time Complexity with Multi-Dimensional Affine Ranking Functions

A standard method for proving the termination of a flowchart program is to exhibit a ranking function, i.e., a function from the program states to a well-founded set, which strictly decreases at each program step. Our main contribution is to give an efficient algorithm for the automatic generation of multi-dimensional affine nonnegative ranking functions, a restricted class of ranking functions that can be handled with linear programming techniques. Our algorithm is based on the combination of the generation of invariants (a technique from abstract interpretation) and on an adaptation of multi-dimensional affine scheduling (a technique from automatic parallelization). We also prove the completeness of our technique with respect to its input and the class of rankings we consider. Finally, as a byproduct, by computing the cardinal of the range of the ranking function, we obtain an upper bound for the computational complexity of the source program, which does not depend on restrictions on the shape of loops or on program structure. This estimate is a polynomial, which means that we can handle programs with more than linear complexity. The method is tested on a large collection of test cases from the literature. We also point out future improvements to handle larger programs

On the Termination of Linear and Affine Programs over the Integers

The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most complete response to this issue: we show that termination for affine programs over Z is decidable under an assumption holding for almost all affine programs, except for an extremely small class of zero Lesbegue measure. We use the notion of asymptotically non-terminating initial variable values} (ANT, for short) for linear loop programs over Z. Those values are directly associated to initial variable values for which the corresponding program does not terminate. We reduce the termination problem of linear affine programs over the integers to the emptiness check of a specific ANT set of initial variable values. For this class of linear or affine programs, we prove that the corresponding ANT set is a semi-linear space and we provide a powerful computational methods allowing the automatic generation of these $ANT$ sets. Moreover, we are able to address the conditional termination problem too. In other words, by taking ANT set complements, we obtain a precise under-approximation of the set of inputs for which the program does terminate.Comment: arXiv admin note: substantial text overlap with arXiv:1407.455

Gardening education in early childhood: Important factors supporting the success of implementing it

Preparing children to become the Rabbani, or godly, generation is the parents’ choice when educating their children. In Indonesia, children are seen as an investment in the nation, state and religion as they will become the generation to change civilisation for the better. Through gardening education in nursery school, it is hoped that children’s monotheism and cognitive, psychomotor and affective development will be achieved. This article offers a service-learning program, developed with the aid of agricultural science and early childhood university education, and partnered with a large social charity, Muhammadiyah. Methods used in this program are group discussion forums, gardening education for class teachers and class action by students in the class. The program involves 60 students aged six at a nursery school, Aisyiyah Bustanul Athfal, in East Java Province, Indonesia. This program is important as it involves measurable assessment of the educational model, learning tool requirements, methods of delivery and evaluation of activities. The program and results shared here demonstrate that gardening education can be accomplished at the nursery school level. Gardening tools are needed, but can be modified to suit this age group. Gardening education for these young children is conducted in accordance with pre-prepared lesson plans. Multilevel learning methods, ranging from reading books, telling stories and watching documentaries to practising and reflecting on gardening activities, are part of the success of this type of gardening education. School support for the implementation of this program markedly determined its success