Related papers: Constant-Space, Constant-Randomness Verifiers with…
We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…
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…
This paper provides a bound on the number of numeric operations (fixed or floating point) that can safely be performed before accuracy is lost. This work has important implications for control systems with safety-critical software, as these…
We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak $\log\log n$ space, (ii) $\log\log n$ is a…
Modern language models represent probability distributions over character strings as distributions over (shorter) token strings derived via a deterministic tokenizer, such as byte-pair encoding. While this approach is highly effective at…
In this paper, we investigate the computational and verification power of bounded-error postselecting realtime probabilistic finite state automata (PostPFAs). We show that PostPFAs using rational-valued transitions can do different variants…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…
The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time…
A $d$-limited automaton is a Turing machine that may rewrite each input cell at most~$d$ times. Hibbard (1967) showed that for every $d \geq 2$ such automata recognize all context-free languages and that deterministic $d$-limited automata…
Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible…
We introduce for the first time a neural-certificate framework for continuous-time stochastic dynamical systems. Autonomous learning systems in the physical world demand continuous-time reasoning, yet existing learnable certificates for…
We study Turing machines that are allowed absolutely no space overhead. The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
Affine finite automata (AfA) can be more succinct than probabilistic and quantum finite automata when recognizing some regular languages with bounded-error. In this paper, we improve previously known constructions given for the succinctness…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
We study the recursion-theoretic complexity of Positive Almost-Sure Termination ($\mathsf{PAST}$) in an imperative programming language with rational variables, bounded nondeterministic choice, and discrete probabilistic choice. A program…
Large language models (LLMs) have demonstrated remarkable progress in code generation, but many existing benchmarks are approaching saturation and offer little guarantee on the trustworthiness of the generated programs. To improve…
Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires…