Related papers: Turing's Landscape: decidability, computability an…
In the 60's, Berger famously showed that translational tilings of $\mathbb{Z}^2$ with multiple tiles are algorithmically undecidable. Recently, Bhattacharya proved the decidability of translational monotilings (tilings by translations of a…
Let $\mathbf{A}$ be a finite algebra generating a finitely decidable variety and having nontrivial strongly solvable radical $\tau$. We provide an improved bound on the number of variables in which a term can be sensitive to changes within…
Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
In light of recent discussions of the string landscape, it is essential to understand the degree to which string theory is predictive. We argue that it is unlikely that the landscape as a whole will exhibit unique correlations amongst…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
The suggestion that there exist causally disconnected universes or sub-universes to explain the values of physical parameters such as the cosmological constant is discussed. A statistical model of the string landscape/topography is…
In hep-th/0501082, a field theoretic ``toy model'' for the Landscape was proposed. We show that the considerations of that paper carry through to realistic effective Lagrangians, such as those that emerge out of string theory. Extracting…
The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We present evidence that the number of string/$M$ theory vacua consistent with experiments is a finite number. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems.
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
We study the decidability and expressiveness issues of $\mu$-calculus on data words and data $\omega$-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment…
We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $ \alpha\in\omega+1\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $…