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In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to…
Recent large language models (LLMs) achieve impressive performance in source-conditioned text generation but often fail to correctly provide fine-grained attributions for their outputs, undermining verifiability and trust. Moreover,…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The automatic generation of computer programs is one of the main applications with practical relevance in the field of evolutionary computation. With program synthesis techniques not only software developers could be supported in their…
Large Language Models (LLMs) are showing remarkable performance in generating source code, yet the generated code often has issues like compilation errors or incorrect code. Researchers and developers often face wasted effort in…
Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike…
The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
Multi Expression Programming (MEP) is a Genetic Programming variant which encodes multiple solutions in a single chromosome. This paper introduces and deeply describes several strategies for solving binary and multi-class classification…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
Generating high-quality code that solves complex programming tasks is challenging, especially with current decoder-based models that produce highly stochastic outputs. In code generation, even minor errors can easily break the entire…
A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from…
We present the notion of asymptotically non-terminating initial variable values for linear loop programs. Those values are directly associated to initial variable values for which the corresponding program does not terminate. Our…