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rqcayley.tex
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rqcayley.tex
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\documentclass[a4paper,numberwithinsect,USenglish]{lipics-v2018}
\usepackage[utf8]{inputenc}
\usepackage[fleqn]{amsmath}
\usepackage{amssymb}
\usepackage{todonotes}
\usepackage{stmaryrd}
\usepackage{hyperref}
\usepackage{amsopn}
\usepackage{mathtools}
\usepackage{algpseudocode}
\usepackage{cite}
\usepackage{thmtools}
\usepackage{thm-restate}
\usepackage{mathabx}
\usepackage{float}
\usetikzlibrary{decorations,arrows,snakes}
%opening
\title{The Cayley-Graph of the Queue Monoid: Logic and Decidability}
\titlerunning{The Cayley-Graph of the Queue Monoid: Logic and Decidability}
\author{Faried Abu Zaid}{Technische Universität Ilmenau, Automata and Logics Group}{[email protected]}{}{}
\author{Chris Köcher}{Technische Universität Ilmenau, Automata and Logics Group}{[email protected]}{https://orcid.org/0000-0003-4575-9339}{}
\authorrunning{F. Abu Zaid, C. Köcher}
\Copyright{Faried Abu Zaid, Chris Köcher}
\subjclass{Theory of computation $\rightarrow$ Logic, Theory of computation $\rightarrow$ Models of computation, Information systems $\rightarrow$ Data structures}
\keywords{Queues, Transformation Monoid, Cayley-Graph, Logic, First-Order Theory, MSO Theory, Model Checking}
%\funding{Partially supported by the DFG-Project ``Speichermechanismen als Monoide'', KU 1107/9-1.}
\EventEditors{Sumit Ganguly and Paritosh Pandya}
\EventNoEds{2}
\EventLongTitle{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}
\EventShortTitle{FSTTCS 2018}
\EventAcronym{FSTTCS}
\EventYear{2018}
\EventDate{December 11--13, 2018}
\EventLocation{Ahmedabad, India}
\EventLogo{}
\SeriesVolume{122}
\ArticleNo{9}
%theorems
\theoremstyle{plain}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{observation}[theorem]{Observation}
\declaretheorem[name=Theorem,numberlike=theorem]{mythm}
\declaretheorem[name=Lemma,numberlike=theorem]{mylem}
\declaretheorem[name=Corollary,numberlike=theorem]{mycor}
\theoremstyle{remark}
\newtheorem*{notation}{Notation}
\makeatletter
\newcommand{\@abbrev}[3]{
\def\c@a@def##1{
\if ##1.
\relax
\else
\@ifdefinable{\@nameuse{#1##1}}{\@namedef{#1##1}{#2##1}}
\expandafter\c@a@def
\fi
}
\c@a@def #3.
}
\@abbrev{bb}{\mathbb}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\@abbrev{bf}{\mathbf}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\@abbrev{bit}{\boldsymbol}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\@abbrev{cal}{\mathcal}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\@abbrev{frak}{\mathfrak}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\@abbrev{rm}{\mathrm}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\@abbrev{scr}{\mathscr}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\@abbrev{sf}{\mathsf}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\@abbrev{ov}{\ov}{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}
\makeatother
% Math Operators, Abbreviations for certain Logic etc.
\DeclareMathOperator{\code}{code}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\tower}{tower}
\DeclareMathOperator{\bin}{bin}
\DeclareMathOperator{\un}{un}
\DeclareMathOperator{\lexp}{lexp}
\DeclareMathOperator{\rexp}{rexp}
\DeclareMathOperator{\pref}{pref}
\DeclareMathOperator{\suf}{suf}
\DeclareMathOperator{\cpr}{rc}
\DeclareMathOperator{\qr}{qr}
%definitions
\newcommand{\ov}[1]{\overline{#1}}
\newcommand{\classfont}[1]{\mathsf{#1}}
\newcommand{\nf}{\classfont{nf}}
\newcommand{\ol}{\classfont{ol}}
\newcommand{\NF}{\classfont{NF}}
\newcommand{\einschr}[2]{\ensuremath{#1|_{#2}}}
\newcommand{\partition}[2]{\ensuremath{#1/_{\!#2}}}
\newcommand{\shuffle}[2]{\!\left\langle#1,\ov{#2}\right\rangle\!}
\newcommand{\rd}[1]{\mathsf{rd}(#1)}
\newcommand{\wrt}[1]{\mathsf{wrt}(#1)}
\newcommand{\strt}[1]{\ov{\pi}_1(#1)}
\newcommand{\shffl}[1]{\ov{\pi}_2(#1)}
\newcommand{\nfx}[2][]{\nf_{#1}(#2)}
\newcommand{\NFx}[1][]{\NF_{#1}}
\newcommand{\olx}[3][]{\ol_{#1}\!\left(#2,#3\right)}
\newcommand{\equivx}[1][]{\equiv_{#1}}
\newcommand{\Qx}{\calQ}
\newcommand{\transx}[1][]{\vdash_{#1}}
\newcommand{\opx}[1][]{\circ_{#1}}
\newcommand{\Rx}[1][]{\mathcal{R}_{#1}}
\newcommand{\leqx}[1][]{\leq_{#1}}
\newcommand{\teilwx}[1][]{\preceq_{#1}}
\newcommand{\chr}[1]{\chi(#1)}
\newcommand{\Chr}[1]{\Chi}
\newcommand{\inv}[1]{#1^{-1}}
\newcommand{\wrti}[1]{\inv{\mathsf{wrt}}\!\left(#1\right)}
\newcommand{\rdi}[1]{\inv{\mathsf{rd}}\!\left(#1\right)}
\newcommand{\FO}{\classfont{FO}}
\newcommand{\MSO}{\classfont{MSO}}
\newcommand{\FOQ}{\FO[(E_\alpha)_{\alpha\in\varSigma}]}
\newcommand{\MSOQ}{\MSO[(E_\alpha)_{\alpha\in\varSigma}]}
\newcommand{\lft}[1]{\lambda(#1)}
\newcommand{\mddl}[1]{\mu(#1)}
\newcommand{\rght}[1]{\varrho(#1)}
\newcommand{\cayley}[2]{\frakC(#1,#2)}
\newcommand{\lcayley}[2]{\mathfrak{LC}(#1,#2)}
\newcommand{\cQ}{\frakC}
\newcommand{\lcQ}{\mathfrak{LC}}
\newcommand{\FOTh}[1]{\classfont{FOTh}(#1)}
\newcommand{\MSOTh}[1]{\classfont{MSOTh}(#1)}
\newcommand{\grL}{\mathcal{L}}
\newcommand{\grR}{\mathcal{R}}
\newcommand{\presuf}{\mathbin{\substack{{\prec}\\{\sqsubsetneq}}}}
\newcommand{\presufeq}{\mathbin{\substack{{\prec}\\{\sqsubseteq}}}}
\newcommand{\ud}[1]{\mathsf{ud}(#1)}
\newcommand{\leqlog}{\leq_{\operatorname{log}}}
\newcommand{\eqlog}{\approx_{\operatorname{log}}}
\renewcommand{\root}[1]{\sqrt{#1}}
\renewcommand{\phi}{\varphi}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\theta}{\vartheta}
\renewcommand{\rho}{\varrho}
\renewcommand{\Gamma}{\varGamma}
\renewcommand{\Sigma}{\varSigma}
\begin{document}
\maketitle
\begin{abstract}
\input{sections/0-abstract}
\end{abstract}
\input{sections/1-introduction}
\input{sections/2-preliminaries}
\input{sections/3-queuemonoid}
\input{sections/4-wordcomb}
\input{sections/5-decidability}
\input{sections/6-conclusion}
\bibliographystyle{plainurl}
\bibliography{sections/lit}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: