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We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
Research must be reproducible in order to make an impact on science and to contribute to the body of knowledge in our field. Yet studies have shown that 70% of research from academic labs cannot be reproduced. In software engineering, and…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
(CROPPED TO FIT IN ARXIV'S SILLY LIMIT. SEE PDF FOR COMPLETE ABSTRACT.) We are the first to thoroughly explore a large space of formal secure compilation criteria based on robust property preservation, i.e., the preservation of properties…
In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works…
This article presents resource-guided synthesis, a technique for synthesizing recursive programs that satisfy both a functional specification and a symbolic resource bound. The technique is type-directed and rests upon a novel type system…
A hyperproperty relates executions of a program and is used to formalize security objectives such as confidentiality, non-interference, privacy, and anonymity. Formally, a hyperproperty is a collection of allowable sets of executions. A…
This paper presents the design and validation of a retrieval-based assistant that supports safety assessment, certification activities, and regulatory compliance for unmanned aircraft systems. The work is motivated by the growing complexity…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…
We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving…
We consider the challenge of finding a deterministic policy for a Markov decision process that uniformly (in all states) maximizes one reward subject to a probabilistic constraint over a different reward. Existing solutions do not fully…
In this paper, we focus on the problem of dynamically analysing concurrent software against high-level temporal specifications. Existing techniques for runtime monitoring against such specifications are primarily designed for sequential…
When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in…
Deploying deep reinforcement learning in safety-critical settings requires developing algorithms that obey hard constraints during exploration. This paper contributes a first approach toward enforcing formal safety constraints on end-to-end…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
Ensuring safety is a crucial challenge when deploying reinforcement learning (RL) to real-world systems. We develop confidence-based safety filters, a control-theoretic approach for certifying state safety constraints for nominal policies…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by…