Related papers: Probabilistic verifiers for asymmetric debates

We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…

We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…

We study the power of polynomial-time truthful mechanisms comparing to polynomial time (non-truthful) algorithms. We show that there is a setting in which deterministic polynomial-time truthful mechanisms cannot guarantee a bounded…

Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…

Despite recent concerns about undesirable behaviors generated by large language models (LLMs), including non-factual, biased, and hateful language, we find LLMs are inherent multi-task language checkers based on their latent representations…

Abstract State Machines (ASMs) provide a model of computations on structures rather than strings. Blass, Gurevich and Shelah showed that deterministic PTIME-bounded ASMs define the choiceless fragment of PTIME, but cannot capture PTIME. In…

This article introduces probabilistic disjunctive normal forms (PDNFs) as a framework for representing and reasoning about uncertainty in logical systems. Unlike classical DNFs, PDNFs assign real-valued weights to variables, encoding…

Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…

Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify…

In the context of investigative journalism, we address the problem of automatically identifying which claims in a given document are most worthy and should be prioritized for fact-checking. Despite its importance, this is a relatively…

Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this…

We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a…

Machine reading comprehension with unanswerable questions aims to abstain from answering when no answer can be inferred. In addition to extract answers, previous works usually predict an additional "no-answer" probability to detect…

There has been a growing interest in defining models of automata enriched with time, such as finite automata extended with clocks (timed automata). In this paper, we study deterministic timed finite state machines (TFSMs), i.e., finite…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

Multi-persona debate systems powered by large language models (LLMs) show promise in reducing confirmation bias, which can fuel echo chambers and social polarization. However, empirical evidence remains limited on whether they meaningfully…

Test-time computation has become a primary driver of progress in large language model (LLM) reasoning, but it is increasingly bottlenecked by expensive verification. In many reasoning systems, a large fraction of verifier calls are spent on…

For some problems, humans may not be able to accurately judge the goodness of AI-proposed solutions. Irving et al. (2018) propose that in such cases, we may use a debate between two AI systems to amplify the problem-solving capabilities of…

We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two…

We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…