Related papers: Pushdown dimension
Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…
A three-way (resp., two-way) two-dimensional automaton has a read-only input head that moves in three (resp., two) directions on a finite array of cells labelled by symbols of the input alphabet. Restricting the input head movement of a…
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This…
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a…
The edit distance between two words $w_1, w_2$ is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform $w_1$ to $w_2$. The edit distance generalizes to languages $\mathcal{L}_1,…
In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state dimension (a finite-state version of algorithmic dimension) of a sequence $S \in \Sigma^\infty$ and, in 2018, Case and Lutz defined and investigated the…
Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This…
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…
A word $w$ is called a reaching word of a subset $S$ of states in a deterministic finite automaton (DFA) if $S$ is the image of $Q$ under the action of $w$. A DFA is called completely reachable if every non-empty subset of the state set has…
In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure,…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
The dimension is a key measure of complexity of partially ordered sets. Small dimension allows succinct encoding. Indeed if $P$ has dimension $d$, then to know whether $x \leq y$ in $P$ it is enough to check whether $x\leq y$ in each of the…
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…
We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
Understanding the self-directed learning complexity has been an important problem that has captured the attention of the online learning theory community since the early 1990s. Within this framework, the learner is allowed to adaptively…