相关论文: Self-Specifying Machines
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We are interested in the following validation problem for computational reductions: for algorithmic problems $P$ and $P^\star$, is a given candidate reduction indeed a reduction from $P$ to $P^\star$? Unsurprisingly, this problem is…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
Large language models have recently demonstrated remarkable abilities to self-correct their responses through iterative refinement, often referred to as self-consistency or self-reflection. However, the dynamics of this self-correction…
Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. Among such…
When learning a new skill, you take advantage of your preexisting skills and knowledge. For instance, if you are a skilled violinist, you will likely have an easier time learning to play cello. Similarly, when learning a new language you…
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…
In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the…
We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting. In this article, we relax the notion of accepting run by allowing a certain quantity…
Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the…
Societal bias towards certain communities is a big problem that affects a lot of machine learning systems. This work aims at addressing the racial bias present in many modern gender recognition systems. We learn race invariant…
We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…
At first glance, one-state Turing machines are very weak: the halting problem for them is decidable, and, without memory, they cannot even accept a simple one element language such as $L = \{ 1 \}$ . Nevertheless it has been showed that a…
A typical desideratum for quantifying the uncertainty from a classification model as a prediction set is class-conditional singleton set calibration. That is, such sets should map to the output of well-calibrated selective classifiers,…
Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we…
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…
Personalized alignment aims to adapt large language models to heterogeneous user preferences, yet the precise theoretical conditions for its statistical efficiency have not been formally established. This paper characterizes the conditions…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.…