Hyphenates polynomial-time when used as an adjective.

introduction.tex

@@ -19,7 +19,7 @@ \section{Introduction}
 %
 %%% relevant existing work, given as part of the need
 For quasigroups, the previous best algorithm for computing the rank requires polynomial time in addition to a polylogarithmic amount of nondeterministic bits.
-For groups, the previous best algorithm for computing the rank requires a polylogarithmic amount of space, which induces a superpolynomial time (hence, inefficient) algorithm.
+For groups, the previous best algorithm for computing the rank requires a polylogarithmic amount of space, which induces a superpolynomial-time (hence, inefficient) algorithm.
 Only for certain classes of finite groups is there a polynomial-time algorithm.
 % task (focus on author) why me? - what was undertaken to address the need
 We improve the best upper bound on the complexity of the rank problem for quasigroups and groups by using an algorithm with limited nondeterminism.

magmarank.tex

@@ -142,7 +142,7 @@ \section{Computation of magma rank}\label{sec:rank}
 We conclude this section with a few observations about \autoref{thm:rank}.
 First, in this proof, we did not use the reduction from \textsc{Quasigroup Rank} to \textsc{Bounded Subquasigroup Membership}, because the closure of $\bFOLL$ under $\bAC^0$ conjunctive truth-table reductions is $\NFOLL$, that is, $\FOLL$ with a polynomial amount of nondeterminism, whereas the closure of $\FOLL$ under the same reductions is $\bFOLL$, a subset of $\NFOLL$.
 
-Second, a slight generalization of \autocite[Theorem~7]{py96} already proves that \textsc{Magma Rank} is in (and complete for) the class of problems decidable by a polynomial time Turing machine with $O(n \log n)$ nondeterministic bits.
+Second, a slight generalization of \autocite[Theorem~7]{py96} already proves that \textsc{Magma Rank} is in (and complete for) the class of problems decidable by a polynomial-time Turing machine with $O(n \log n)$ nondeterministic bits.
 We have nevertheless included the fact that \textsc{Magma Rank} is in $\NP$ to highlight the general strategy for proving these upper bounds for each class of algebraic structure.
 
 Third, we can almost show a reduction in the opposite direction of \autoref{lem:ranktomem}.

preliminaries.tex

@@ -128,7 +128,7 @@ \subsection{Algebra}
 
   Unlike for the Latin square property in the previous example, there is no obvious way to tell whether a binary operation is associative simply by scanning the rows and columns.
   In other words, given only its Cayley table, determining whether a magma is a quasigroup \emph{seems} easier than determining whether a magma is a semigroup.
-  However, there is a polynomial time algorithm, attributed to F.~W.~Light, for deciding whether a magma is associative; it is simply the naïve algorithmic implementation of the associativity condition.
+  However, there is a polynomial-time algorithm, attributed to F.~W.~Light, for deciding whether a magma is associative; it is simply the naïve algorithmic implementation of the associativity condition.
 \end{example}
 
 \begin{example}