439 %(in \textit{ALTS}) |
439 %(in \textit{ALTS}) |
440 |
440 |
441 \noindent |
441 \noindent |
442 where $bs$ stands for bitcodes, $a$ for $\bold{a}$nnotated regular |
442 where $bs$ stands for bitcodes, $a$ for $\bold{a}$nnotated regular |
443 expressions and $as$ for a list of annotated regular expressions. |
443 expressions and $as$ for a list of annotated regular expressions. |
444 The alternative constructor($\textit{ALTS}$) has been generalized to |
444 The alternative constructor($\oplus$) has been generalized to |
445 accept a list of annotated regular expressions rather than just 2. |
445 accept a list of annotated regular expressions rather than just 2. |
446 We will show that these bitcodes encode information about |
446 We will show that these bitcodes encode information about |
447 the (POSIX) value that should be generated by the Sulzmann and Lu |
447 the (POSIX) value that should be generated by the Sulzmann and Lu |
448 algorithm. |
448 algorithm. |
449 |
449 |
454 defined as follows: |
454 defined as follows: |
455 |
455 |
456 %\begin{definition} |
456 %\begin{definition} |
457 \begin{center} |
457 \begin{center} |
458 \begin{tabular}{lcl} |
458 \begin{tabular}{lcl} |
459 $(\ZERO)^\uparrow$ & $\dn$ & $\textit{ZERO}$\\ |
459 $(\ZERO)^\uparrow$ & $\dn$ & $\ZERO$\\ |
460 $(\ONE)^\uparrow$ & $\dn$ & $\textit{ONE}\,[]$\\ |
460 $(\ONE)^\uparrow$ & $\dn$ & $_{[]}\ONE$\\ |
461 $(c)^\uparrow$ & $\dn$ & $\textit{CHAR}\,[]\,c$\\ |
461 $(c)^\uparrow$ & $\dn$ & $_{[]}{\bf c}$\\ |
462 $(r_1 + r_2)^\uparrow$ & $\dn$ & |
462 $(r_1 + r_2)^\uparrow$ & $\dn$ & |
463 $\textit{ALTS}\;[]\,List((\textit{fuse}\,[\Z]\,r_1^\uparrow),\, |
463 $_{[]}\oplus[\textit{fuse}\,[0]\,r_1^\uparrow,\, |
464 (\textit{fuse}\,[\S]\,r_2^\uparrow))$\\ |
464 \textit{fuse}\,[1]\,r_2^\uparrow]$\\ |
465 $(r_1\cdot r_2)^\uparrow$ & $\dn$ & |
465 $(r_1\cdot r_2)^\uparrow$ & $\dn$ & |
466 $\textit{SEQ}\;[]\,r_1^\uparrow\,r_2^\uparrow$\\ |
466 $_{[]}r_1^\uparrow \cdot r_2^\uparrow$\\ |
467 $(r^*)^\uparrow$ & $\dn$ & |
467 $(r^*)^\uparrow$ & $\dn$ & |
468 $\textit{STAR}\;[]\,r^\uparrow$\\ |
468 $_{[]}(r^\uparrow)^*$\\ |
469 \end{tabular} |
469 \end{tabular} |
470 \end{center} |
470 \end{center} |
471 %\end{definition} |
471 %\end{definition} |
472 |
472 |
473 \noindent |
473 \noindent |