power series removed

Author: peterthiemann

intro.tex

@@ -51,8 +51,9 @@ \section{Introduction}
 that certainly do not match a given (extended) regular expression.
 
 Our algorithms produce lazy streams, which are guaranteed to be
-productive. A user can gauge the string size or the
-number of generated strings without risking partiality.
+productive (i.e., their next element is computed in finite time). A
+user can limit the string length or the number of generated strings
+without risking partiality.
 
 Source code for implementations in Haskell and in OCaml is available
 on GitHub. Examples can be run in a Web App.\footnote{%

main.tex

@@ -1,7 +1,7 @@
 \newif\ifsubmit
 \submitfalse
 %% 12 pp + bib
-\documentclass[sigplan,review,anonymous]{acmart}%
+\documentclass[sigplan,authorversion]{acmart}%
 \settopmatter{printfolios=true,printccs=false,printacmref=false}
 
 % Encoding and lang

motivation.tex

@@ -338,17 +338,13 @@ \section{Generation by Cross Section}
 \textbf{$n^{th}$ segment of $L$} is $L_n := L \cap \Sigma^n$, the set of
 words of length $n$ in $L$. As $L = \bigcup_{n\ge0} L_n$ we
 define the \textbf{segment representation of $L$} by the
-sequence of all segments, which we can write formally as a
-power series\footnote{These power series are different
-  from formal power series used in formal language theory
-  \cite{DBLP:books/daglib/0067812,DBLP:books/sp/KuichS86}.}
-\begin{gather*}
-  L = \Sigma_{n=0}^\infty L_nx^n\text.
-\end{gather*}
+sequence of all segments $(L_n)_{n\ge0}$.
+% \begin{gather*}
+%   L = \Sigma_{n=0}^\infty L_nx^n\text.
+% \end{gather*}
 
 The language operations can be expressed on this representation by
-standard operations on power series over semirings
-$(\Power(\Sigma^*),\cup,\cdot)$ and $(\Power(\Sigma^*), \cup, \cap)$.
+standard operations on sequences.
 \begin{align}
   \label{eq:3}
   &\text{Sum:}
@@ -361,9 +357,7 @@ \section{Generation by Cross Section}
   & (U \cdot V)_n &= \bigcup_{i=0}^n U_i\cdot V_{n-i}
 \end{align}
 
-By applying
-the usual spiel of representing a power series by its sequence of
-coefficients, all operations become executable.
+In a language that supports streams, all operations become executable.
 %
 As the alphabet $\Sigma$ is finite, each segment $L_n$ is a finite set. Hence, the sum and
 Hadamard product yield efficient definitions of language union and intersection. Due to
@@ -423,16 +417,16 @@ \section{Generation by Cross Section}
 \paragraph{Kleene Closure}
 It is well known that $U^* = (U\setminus\{\varepsilon\})^*$. 
 Hence, a simple calculation yields an
-effective algorithm for computing the coefficients of the power series for $U^*$. 
+effective algorithm for computing the sequence of cross sections for $U^*$. 
 \begin{align}
   \label{eq:2}
   &%\text{Star:}
   & (U^*)_0 &= 1
   & (U^*)_n &= (U \cdot U^*)_n = \bigcup_{i=1}^n U_i\cdot (U^*)_{n-i}
 \end{align}
 The key observation is that Equation~\eqref{eq:2} is a proper
-inductive definition of the power series for $U^*$. It never touches $U_0$ and the union
-only touches the coefficients $(U^*)_{n-1}$ down to $(U^*)_0$. Hence, $(U^*)_n$ is well
+inductive definition of the sequence for $U^*$. It never touches $U_0$ and the union
+only touches the elements $(U^*)_{n-1}$ down to $(U^*)_0$. Hence, $(U^*)_n$ is well
 defined as it only relies on $U$ and previously computed indexes!
 
 \begin{figure}[tp]
@@ -484,7 +478,7 @@ \section{Generation by Cross Section}
 
 Productivity: We can generate productive segment
 representations from all extended regular expressions. The implementation of each
-operation is guided by corresponding operations on power series.
+operation is guided by corresponding operations on streams.
 
 Easy Gauging: To restrict the generated segmented output, say \code{segs}, to words of
 length less than a given 

ocaml.tex

@@ -15,7 +15,7 @@ \section{\ocaml Implementation}
 and various data structures for segments. 
 The key idea is that the internal order on words in a segment does not matter
 because each segment only contains words of the same length.
-All we need is a data structure that supports the power series
+All we need is a data structure that supports the stream
 operations.
 %
 To facilitate such experimentation, we implemented the