Related papers: Algebra-based Loop Synthesis

Program invariants are important for defect detection, program verification, and program repair. However, existing techniques have limited support for important classes of invariants such as disjunctions, which express the semantics of…

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…

Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be…

We present new algorithms to synthesize exact universal reversible gate library for various types of gates and costs. We use the powerful algebraic software GAP for implementation and examination of our algorithms and the reversible logic…

We present an efficient approach to prove termination of monotone programs with integer variables, an expressive class of loops that is often encountered in computer programs. Our approach is based on a lightweight static analysis method…

Fast numerical libraries have been a cornerstone of scientific computing for decades, but this comes at a price. Programs may be tied to vendor specific software ecosystems resulting in polluted, non-portable code. As we enter an era of…

Synthesis of program parts is very useful for concurrent systems. However, most synthesis approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system.…

We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear…

Program verification relies on loop invariants, yet automatically discovering strong invariants remains a long-standing challenge. We investigate whether large language models (LLMs) can accelerate program verification by generating useful…

Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…

The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…

When giving automated feedback to a student working on a beginner's exercise, many programming tutors run into a completeness problem. On the one hand, we want a student to experiment freely. On the other hand, we want a student to write…

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…

We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases of the Bayesian posterior of a synthesis problem. This new…

We consider the problem of generating automatic code given sample input-output pairs. We train a neural network to map from the current state and the outputs to the program's next statement. The neural network optimizes multiple tasks…

Synthesis of reversible logic circuits has gained great atten- tion during the last decade. Various synthesis techniques have been pro- posed, some generate optimal solutions (in gate count) and are termed as exact, while others are…

The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a…

In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…

The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…