Related papers: (Un)Solvable Loop Analysis
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com putations update internal states and…
Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We…
Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
One of the obstacles in automatic program proving is to obtain suitable loop invariants. The invariant of a loop is a weakened form of its postcondition (the loop's goal, also known as its contract); the present work takes advantage of this…
In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation,…
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing…
Morgan and McIver's weakest pre-expectation framework is one of the most well-established methods for deductive verification of probabilistic programs. Roughly, the idea is to generalize binary state assertions to real-valued expectations,…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
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…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…
In this paper we study the robust invariant sets generation problem for discrete-time switched polynomial systems subject to disturbance inputs within the optimal control framework. A robust invariant set of interest is a set of states such…
In the verification of loop programs, disjunctive invariants are essential to capture complex loop dynamics such as phase and mode changes. In this work, we develop a novel approach for the automated generation of affine disjunctive…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…
In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a…
We present a novel algorithm that synthesizes imperative programs for introductory programming courses. Given a set of input-output examples and a partial program, our algorithm generates a complete program that is consistent with every…