alphaCertified: certifying solutions to polynomial systems

Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements algorithms based on alpha-theory to certify solutions to polynomial systems using both exact rational arithmetic and arbitrary precision floating point arithmetic. It also implements an algorithm to certify whether a given point corresponds to a real solution to a real polynomial system, as well as algorithms to heuristically validate solutions to overdetermined systems. Examples are presented to demonstrate the algorithms.Comment: 21 page

Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

Summary-based inference of quantitative bounds of live heap objects

This article presents a symbolic static analysis for computing parametric upper bounds of the number of simultaneously live objects of sequential Java-like programs. Inferring the peak amount of irreclaimable objects is the cornerstone for analyzing potential heap-memory consumption of stand-alone applications or libraries. The analysis builds method-level summaries quantifying the peak number of live objects and the number of escaping objects. Summaries are built by resorting to summaries of their callees. The usability, scalability and precision of the technique is validated by successfully predicting the object heap usage of a medium-size, real-life application which is significantly larger than other previously reported case-studies.Fil: Braberman, Victor Adrian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garbervetsky, Diego David. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hym, Samuel. Universite Lille 3; FranciaFil: Yovine, Sergio Fabian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Inferring Energy Bounds via Static Program Analysis and Evolutionary Modeling of Basic Blocks

The ever increasing number and complexity of energy-bound devices (such as the ones used in Internet of Things applications, smart phones, and mission critical systems) pose an important challenge on techniques to optimize their energy consumption and to verify that they will perform their function within the available energy budget. In this work we address this challenge from the software point of view and propose a novel parametric approach to estimating tight bounds on the energy consumed by program executions that are practical for their application to energy verification and optimization. Our approach divides a program into basic (branchless) blocks and estimates the maximal and minimal energy consumption for each block using an evolutionary algorithm. Then it combines the obtained values according to the program control flow, using static analysis, to infer functions that give both upper and lower bounds on the energy consumption of the whole program and its procedures as functions on input data sizes. We have tested our approach on (C-like) embedded programs running on the XMOS hardware platform. However, our method is general enough to be applied to other microprocessor architectures and programming languages. The bounds obtained by our prototype implementation can be tight while remaining on the safe side of budgets in practice, as shown by our experimental evaluation.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854). Improved version of the one presented at the HIP3ES 2016 workshop (v1): more experimental results (added benchmark to Table 1, added figure for new benchmark, added Table 3), improved Fig. 1, added Fig.

Live Heap Space Analysis for Languages with Garbage Collection

The peak heap consumption of a program is the maximum size of the live data on the heap during the execution of the program, i.e., the minimum amount of heap space needed to run the program without exhausting the memory. It is well-known that garbage collection (GC) makes the problem of predicting the memory required to run a program difficult. This paper presents, the best of our knowledge, the first live heap space analysis for garbage-collected languages which infers accurate upper bounds on the peak heap usage of a program’s execution that are not restricted to any complexity class, i.e., we can infer exponential, logarithmic, polynomial, etc., bounds. Our analysis is developed for an (sequential) object-oriented bytecode language with a scoped-memory manager that reclaims unreachable memory when methods return. We also show how our analysis can accommodate other GC schemes which are closer to the ideal GC which collects objects as soon as they become unreachable. The practicality of our approach is experimentally evaluated on a prototype implementation.We demonstrate that it is fully automatic, reasonably accurate and efficient by inferring live heap space bounds for a standardized set of benchmarks, the JOlden suite

A generic imperative language for polynomial time

The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative programming. We introduce a new approach to ramification which, among other benefits, adapts readily to fully general imperative programming. The novelty is in ramifying finite second-order objects, namely finite structures, rather than ramifying elements of free algebras. In so doing we bridge between Implicit Complexity's type theoretic characterizations of feasibility, and the data-flow approach of Static Analysis.Comment: 18 pages, submitted to a conferenc