Related papers: A Completeness Theorem for Probabilistic Regular E…
Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, for both foundations and…
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of…
We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
We present power low rank ensembles (PLRE), a flexible framework for n-gram language modeling where ensembles of low rank matrices and tensors are used to obtain smoothed probability estimates of words in context. Our method can be…
Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are…
We aim at a holistic perspective on program logics, including Hoare and incorrectness logics. To this end, we study different classes of properties arising from the generalization of the aforementioned logics. We compare our results with…
In probabilistic grammatical inference, a usual goal is to infer a good approximation of an unknown distribution P called a stochastic language. The estimate of P stands in some class of probabilistic models such as probabilistic automata…
Keyphrase Prediction (KP) is essential for identifying keyphrases in a document that can summarize its content. However, recent Natural Language Processing (NLP) advances have developed more efficient KP models using deep learning…
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
The combined universal probability $\mathbf{m}(D)$ of strings $x$ in sets $D$ is close to max $\mathbf{m}(x)$ over $x$ in $D$: their logs differ by at most $D$'s information $\mathbf{I}(D:\mathcal{H})$ about the halting sequence…
We give a decision procedure and proof of correctness for the equational theory of probabilistic Kleene algebra with angelic nondeterminism introduced in Ong, Ma, and Kozen (2025).
Our aim is to construct a finite automaton recognizing the set of words that are at a bounded distance from some word of a given regular language. We define new regular operators, the similarity operators, based on a generalization of the…
We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on…
Probabilistic programming languages aim to describe and automate Bayesian modeling and inference. Modern languages support programmable inference, which allows users to customize inference algorithms by incorporating guide programs to…
We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties…
Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean…