Related papers: Descriptive complexity of real computation and pro…
interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…
This paper argues that the judicial use of formal language theory and grammatical inference are invaluable tools in understanding how deep neural networks can and cannot represent and learn long-term dependencies in temporal sequences.…
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…
Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…
We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
We prove in this paper that there is a language $L_s$ accepted by some nondeterministic Turing machine that runs within time $O(n^k)$ for any positive integer $k\in\mathbb{N}_1$ but not by any ${\rm co}\mathcal{NP}$ machines. Then we…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
In a \emph{separability problem}, we are given two sets $K$ and $L$ from a class $\mathcal{C}$, and we want to decide whether there exists a set $S$ from a class $\mathcal{S}$ such that $K\subseteq S$ and $S\cap L=\emptyset$. In this case,…
An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly…
We present efficient algorithms to reduce the size of nondeterministic B\"uchi word automata (NBA) and nondeterministic finite word automata (NFA), while retaining their languages. Additionally, we describe methods to solve PSPACE-complete…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models.…
By relaxing conditions for natural structure learning algorithms, a family of constraint-based algorithms containing all exact structure learning algorithms under the faithfulness assumption, we define localised natural structure learning…
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…
Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey…
We consider the problem of explaining a class of tractable deep probabilistic models, the Sum-Product Networks (SPNs) and present an algorithm ExSPN to generate explanations. To this effect, we define the notion of a context-specific…