From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527

Two-way automata and transducers with planar behaviours are aperiodic

We consider a notion of planarity for two-way finite automata and transducers, inspired by Temperley-Lieb monoids of planar diagrams. We show that this restriction captures star-free languages and first-order transductions.Comment: 18 pages, DMTCS submissio

Basic Cable: Notes Toward Digital Ontology

This thesis begins the work of constructing a fundamental ontology that employs the network automaton—a class of abstract computer program—as its model. Following a brief historical overview of the theory of network automata and its culmination in the work of Steven Wolfram, I examine how it bears on the ancient question concerning whether the continuous or the discrete has ontological primacy, consider the ontological status of materiality in consultation with Deleuzean ontology, and introduce the concept of prescience as a means of topologically mapping emergent patterns within the causal relations that compose the network. Finally, I will break the network automaton down even further into its most rudimentary functional operations, and consider preliminarily how this model might be adapted toward an atomistic theory of the subject

Design and Investigation of Genetic Algorithmic and Reinforcement Learning Approaches to Wire Crossing Reductions for pNML Devices

Perpendicular nanomagnet logic (pNML) is an emerging post-CMOS technology which encodes binary data in the polarization of single-domain nanomagnets and performs operations via fringing field interactions. Currently, there is no complete top-down workflow for pNML. Researchers must instead simultaneously handle place-and-route, timing, and logic minimization by hand. These tasks include multiple NP-Hard subproblems, and the lack of automated tools for solving them for pNML precludes the design of large-scale pNML circuits

On the synchronization of finite state automata

Abstract: We study some problems related to the synchronization of finite state automata and the Cˇerny’s conjecture. We focus on the synchronization of small sets of states, and more specifically on the synchronization of triples. We argue that it is the most simple synchronization scenario that exhibits the intricacies of the original Cˇerny’s scenario (all states synchronization). Thus, we argue that it is complex enough to be interesting, and tractable enough to be studied via algo- rithmic tools. We use those tools to establish a long list of facts related to those issues. We observe that planar automata seems to be representative of the synchroniz- ing behavior of deterministic finite state automata. Moreover, we present strong evidence suggesting the importance of planar automata in the study of Cˇerny’s conjecture. We also study synchronization games played on planar automata. We prove that recognizing the planar games that can be won by the synchronizer is a co-NP hard problem. We prove some additional results indicating that pla- nar games are as hard as nonplanar games. Those results amount to show that planar automata are representative of the intricacies of automata synchronization.Doctorad

Quantum Low-Density Parity-Check Codes

Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called “quantum low-density parity-check (LDPC) codes.” The codes we discuss are alternatives to the surface code, which is currently the leading candidate to implement quantum fault tolerance. We introduce the zoo of quantum LDPC codes and discuss their potential for making quantum computers robust with regard to noise. In particular, we explain recent advances in the theory of quantum LDPC codes related to certain product constructions and discuss open problems in the field

Algorithm Engineering for Realistic Journey Planning in Transportation Networks

Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird