Related papers: Linear Loop Synthesis for Quadratic Invariants
The LLM-as-a-judge paradigm enables flexible, user-defined evaluation, but its effectiveness is often limited by the scarcity of diverse, representative data for refining criteria. We present a tool that integrates synthetic data generation…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Automated program repair (APR) faces the challenge of test overfitting, where generated patches pass validation tests but fail to generalize. Existing methods for patch assessment involve generating new tests or manual inspection, which can…
We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…
As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory…
This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no…
Large language models (LLMs) have shown impressive promise in code generation, yet their progress remains limited by the shortage of large-scale datasets that are both diverse and well-aligned with human reasoning. Most existing resources…
We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
To ensure resilience against the unavoidable noise in quantum computers, quantum information needs to be encoded using an error-correcting code, and circuits must have a particular structure to be fault-tolerant. Compilation of…
Several techniques for analysis and transformations are used in compilers. Among them, the peeling of loops for hoisting quasi-invariants can be used to optimize generated code, or simply ease developers' lives. In this paper, we introduce…
We advance here an algorithm of a synthesis of an electric circuit based on prescribed quadratic Lagrangian. That is the circuit evolution equations are equivalent to the relevant Euler-Lagrange equations. The proposed synthesis is a…
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…
Being able to provide counterfactual interventions - sequences of actions we would have had to take for a desirable outcome to happen - is essential to explain how to change an unfavourable decision by a black-box machine learning model…
It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…