Related papers: Constant-Space, Constant-Randomness Verifiers with…
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not…
LLM (large language model) practitioners commonly notice that outputs can vary for the same inputs under settings expected to be deterministic. Yet the questions of how pervasive this is, and with what impact on results, have not to our…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
We consider a general class of decision problems concerning formal languages, called ``(one-dimensional) unboundedness predicates'', for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces…
Verifiers are auxiliary models that assess the correctness of outputs generated by base large language models (LLMs). They play a crucial role in many strategies for solving reasoning-intensive problems with LLMs. Typically, verifiers are…
The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any…
In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks -- small modifications of the input that change the predictions. Besides rigorously studied $\ell_p$-bounded additive…
We develop a declarative DSL - \cf - that can be used to specify Abstract Interpretation-based DNN certifiers. In \cf, programmers can easily define various existing and new abstract domains and transformers, all within just a few 10s of…
We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…
Large Language models (LLMs) can generate complicated source code from natural language prompts. However, LLMs can generate output that deviates from what the user wants, requiring supervision and editing. To support this process, we offer…
We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window $n$ and a stream of symbols. At each time…
Bounded verification has proved useful to detect bugs and to increase confidence in the correctness of a program. In contrast to unbounded verification, reasoning about calls via (bounded) inlining and about loops via (bounded) unrolling…
The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a…
Machine Learning (ML) has become an integral part of our society, commonly used in critical domains such as finance, healthcare, and transportation. Therefore, it is crucial to evaluate not only whether ML models make correct predictions…
{\it Two-way quantum automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous in 2002. In this paper we study state succinctness of 2QCFA. For any $m\in {\mathbb{Z}}^+$ and any $\epsilon<1/2$, we show…
We discuss the problem of learning a deterministic finite automaton (DFA) from a confidence oracle. That is, we are given access to an oracle $Q$ with incomplete knowledge of some target language $L$ over an alphabet $\Sigma$; the oracle…
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…
Adversarial examples pose a security risk as they can alter decisions of a machine learning classifier through slight input perturbations. Certified robustness has been proposed as a mitigation where given an input $\mathbf{x}$, a…
In this note, we generalize the results of arXiv:0901.2703v1 We show that all one-way quantum finite automaton (QFA) models that are at least as general as Kondacs-Watrous QFA's are equivalent in power to classical probabilistic finite…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…