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This work introduces a probabilistic-based model for binary CSP that provides a fine grained analysis of its internal structure. Assuming that a domain modification could occur in the CSP, it shows how to express, in a predictive way, the…
A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of…
We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…
Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational…
Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees…
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…
Existing probabilistic scanners and parsers impose hard constraints on the way lexical and syntactic ambiguities can be resolved. Furthermore, traditional grammar-based parsing tools are limited in the mechanisms they allow for taking…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and…
Squared tensor networks (TNs) and their generalization as parameterized computational graphs -- squared circuits -- have been recently used as expressive distribution estimators in high dimensions. However, the squaring operation introduces…
Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express $p_n(x)$ as a \emph{path integral} in the ``phase space'' $\Space{N}{} \times {[-\pi,\pi]}$. The Hamiltonian…
We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…
In this work, we propose a class of equational theories for bounded binary circuits that have the finite variant property. These theories could serve as a building block to specify cryptographic primitive implementations and automatically…
Grokking has been actively explored to reveal the mystery of delayed generalization and identifying interpretable representations and algorithms inside the grokked models is a suggestive hint to understanding its mechanism. Grokking on…
We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear…