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Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…
Large language models are emerging as scientific assistants, but evaluating their ability to reason from empirical data remains challenging. Benchmarks derived from published studies and human annotations inherit publication bias,…
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…
Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…
Given a specification $\varphi(X,Y)$ over inputs $X$ and output $Y$, defined over a background theory $\mathbb{T}$, the problem of program synthesis is to design a program $f$ such that $Y=f(X)$ satisfies the specification $\varphi$. Over…
Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word…
Counterexample-guided inductive synthesis CEGIS is used to synthesize programs from a candidate space of programs. The technique is guaranteed to terminate and synthesize the correct program if the space of candidate programs is finite. But…
Synthesis automatically constructs an implementation that satisfies a given logical specification. In this paper, we study the live synthesis problem, where the synthesized implementation replaces an already running system. In addition to…
We study the achievable performance of adaptive query procedures for the noisy 20 questions problem with measurement-dependent noise over a unit cube of finite dimension. The performance criterion that we consider is the minimal resolution,…
We introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…
Reactive synthesis, the problem of automatically constructing a hardware circuit from a logical specification, is a long-standing challenge in formal verification. It is elusive for two reasons: It is algorithmically hard, and writing…
We study the problem of simultaneous search for multiple targets over a multidimensional unit cube and derive fundamental resolution limits of non-adaptive querying procedures using the 20 questions estimation framework. The performance…
Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained…
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…
Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate…
Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded,…
This paper proposes relational program synthesis, a new problem that concerns synthesizing one or more programs that collectively satisfy a relational specification. As a dual of relational program verification, relational program synthesis…
Within machine learning, the subfield of Neural Architecture Search (NAS) has recently garnered research attention due to its ability to improve upon human-designed models. However, the computational requirements for finding an exact…