### Small documentation fixes.

* doc/tl/tl.tex: Fix a few typos, and comment a missplaced paragraph.
* doc/tl/tl.bib: Typos.
parent 1a50ae3b
 ... ... @@ -18,11 +18,11 @@ @InProceedings{ beer.01.cav, author = {Ilan Beer and Shoham Ben-David and Cindy Eisner and Dana Fisman and Anna Gringauze and Yoav Rodeh}, title = {The Temporal Logic Sugar}, title = {The Temporal Logic {S}ugar}, booktitle = {Proceedings of the 13th international conferance on Computer Aided Verification (CAV'01)}, series = {Lecture Notes in Computer Science}, editor = {Berry, Gérard and Comon, Hubert and Finkel, Alain}, editor = {Berry, G{\'e}rard and Comon, Hubert and Finkel, Alain}, publisher = {Springer}, isbn = {978-3-540-42345-4}, pages = {363--367}, ... ...
 ... ... @@ -193,7 +193,7 @@ \section{Finite and Infinite Sequences} Let $\N=\{0,1,2,\ldots\}$ designate the set of natural numbers and Let $\N=\{0,1,2,\ldots\}$ denote the set of natural numbers and $\omega\not\in\N$ the first transfinite ordinal. We extend the $<$ relation from $\N$ to $\N\cup\{\omega\}$ with $\forall n\in N,\, n<\omega$. Similarly let us extend the addition and subtraction with ... ... @@ -1005,8 +1005,8 @@ suffix-closed, i.e., if you remove any finite prefix of an accepted $\varphi$ is a suffix-closed formula, then $\G\varphi \equiv \varphi$. Let $\varphi$ designate any arbitrary formula and $\varphi_E$ (resp. $\varphi_U$) designate any instance of a pure eventuality Let $\varphi$ denote any arbitrary formula and $\varphi_E$ (resp. $\varphi_U$) denote any instance of a pure eventuality (resp. a purely universal) formula. We have the following grammar rules: ... ... @@ -1108,9 +1108,9 @@ methods \texttt{is\_syntactic\_safety()}, page~\pageref{property-methods}). The symbols $\varphi_G$, $\varphi_S$, $\varphi_O$, $\varphi_P$, $\varphi_R$ designate any formula belonging respectively to the $\varphi_R$ denot any formula belonging respectively to the Guarantee, Safety, Obligation, Persistence, or Recurrence classes. $\varphi_F$ designates a finite LTL formula (the unnamed class at the $\varphi_F$ denotes a finite LTL formula (the unnamed class at the intersection of Safety and Guarantee formul\ae{} on Fig.~\ref{fig:hierarchy}). $v$ denotes any variable, $r$ any SERE, $r_F$ any bounded SERE (no loops), and $r_I$ any unbounded SERE. ... ... @@ -1164,7 +1164,7 @@ $r_F$ any bounded SERE (no loops), and $r_I$ any unbounded SERE. \mid{}& \X\varphi_R \mid \G\varphi_R \mid \varphi_R\U\varphi_G\mid\varphi_R\R\varphi_R\mid \varphi_R\W\varphi_R\mid\varphi_G\M\varphi_R\\ \mid{}& \sere{r_F}\Esuffix \varphi_R \mid \sere{r_I}\Esuffix \varphi_G\mid \sere{r}\Asuffix \varphi_P\\ \mid{}& \sere{r}\Asuffix \varphi_R\mid \sere{r_F}\Esuffix \varphi_R \mid \sere{r_I}\Esuffix \varphi_G\\ \end{align*} It should be noted that a formula can belong to a class of the ... ... @@ -1293,16 +1293,16 @@ from left to right, as usual): \G(f_1\OR\ldots\OR f_n \OR \G\F(g_1)\OR\ldots\OR \G\F(g_m)) & \equiv \G(f_1\OR\ldots\OR f_n)\OR \G\F(g_1\OR\ldots\OR g_m) \end{align*} Note that the latter three rewriting rules for $\G$ have no dual: rewriting $\F(f \AND \G\F g)$ to $\F(f) \AND \G\F(g)$ (as suggested by~\citet{somenzi.00.cav}) goes against our goal of moving the $\F$ operator in front of the formula. Conceptually, it is also easier to understand $\F(f \AND \G\F g)$: has long as $f$ has not been verified, there is no need to worry about the $\G\F g$ term. % Note that the latter three rewriting rules for $\G$ have no dual: % rewriting $\F(f \AND \G\F g)$ to $\F(f) \AND \G\F(g)$ (as suggested % by~\citet{somenzi.00.cav}) goes against our goal of moving the $\F$ % operator in front of the formula. Conceptually, it is also easier to % understand $\F(f \AND \G\F g)$: has long as $f$ has not been verified, % there is no need to worry about the $\G\F g$ term. Here are the basic rewriting rules for binary operators (excluding $\OR$ and $\AND$ which are considered in Spot as $n$-ary operators). $b$ denotes a Boolean formula. $b$ denotes any Boolean formula. \begin{align*} \1 \U f & \equiv \F f & f \W \0 & \equiv \G f \\ ... ... @@ -1684,8 +1684,8 @@ f)\implies(\pi\VDash g)$. The recursive rules for syntactic implication are rules are described in table~\ref{tab:syntimpl}, in which$\simp$denotes the syntactic implication,$f$,$f_1$,$f_2$,$g$,$g_1$and$g_2$designate any PSL formula in negative normal form, and$f_U$and$g_E$designate a implication,$f$,$f_1$,$f_2$,$g$,$g_1$and$g_2$denote any PSL formula in negative normal form, and$f_U$and$g_E$denot a purely universal formula and a pure eventuality. The form on the left of the table syntactically implies the form on ... ... @@ -1704,7 +1704,7 @@ conclusion by chaining two rules: $\F f \simp \underbrace{\F $f \simp \F g$ \textit{if} $f\simp g$''. The rules from table~\ref{tab:syntimpl} should be completed by the following cases, where $f_b$ and $g_b$ designate Boolean formul\ae{}: following cases, where $f_b$ and $g_b$ denote Boolean formul\ae{}: \begin{center} \begin{tabular}{rl} we have & if \\ ... ...
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