diff --git a/index.pdf b/index.pdf index 18d37d6..0d50e66 100644 Binary files a/index.pdf and b/index.pdf differ diff --git a/index.typ b/index.typ index 5a2d101..c8e584f 100644 --- a/index.typ +++ b/index.typ @@ -10,7 +10,7 @@ = Exercise 01 #let question(body) = block( - fill: luma(240), + fill: luma(255), inset: 8pt, radius: 4pt )[ @@ -139,4 +139,69 @@ We have the following Recursion: - AsignOp: { ";" } - CondTerm: { "&&", Follow(CondTerm) } = { "&&", CondFact } +== 02 Konstruktion einer Grammatik +#question[ +Geben Sie eine EBNF-Grammatik an, die folgende Beschreibung abdeckt. Es handelt sich dabei um eine fiktive +Schachnotation. Bilden Sie dabei beliebig viele Non-Terminalklassen, mindestens jedoch eine für jedes fett +geschriebene Wort. +Ein Spiel setzt sich aus mindestens einem Zug zusammen, wobei Züge durch Beistriche (“,”) getrennt sind. +Nach dem letzten Zug steht ein Strichpunkt (“;”). +Ein Zug beginnt mit einer Figur, gefolgt von einer Position (Startposition). Darauf folgt ein Bindestrich (“-”), +gefolgt von einer weiteren Position (Zielposition). Sollte durch den Zug eine Figur geschlagen worden sein, +folgt ein “x”. Unabhängig davon, ob eine Figur geschlagen wurde, folgt gegebenenfalls die Information, ob der +Gegner Schach ( + ) oder Schach-Matt ( \# ) steht. Ein Spieler kann nicht gleichzeitig Schach und Schach-Matt +stehen. +Beispielzüge: Ka1-a2, Qf5-h7x\#, Pb2-c3x, Rh1-h6+, Bb5-d7x+ +Eine Figur ist entweder ein König (“K”), eine Königin (“Q”), ein Turm (“R”), ein Läufer (“B”), ein Springer +(“N”), oder ein Bauer (“P”). +Eine Position ist eine Spalte, gefolgt von einer Zeile. +Eine Spalte ist ein Buchstabe zwischen a und h (a, b, c, d, e, f, g, h). +Eine Zeile ist eine Zahl zwischen 1 und 8 (1, 2, 3, 4, 5, 6, 7, 8). + +] + +```ebnf +Game = Turn { "," Turn} ";". +Turn = Character Position "-" Position ["x"] ["+" | "#"]. +Character = “K” | “Q” | “R” | “B” | “N” | “P”. +Position = Column Row. +Column = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h". +Row = "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8". +``` + +== 03 Beseitigung von Linksrekursionen + +#question[ + + Wo befinden sich in der folgenden Grammatik Linksrekursionen? Geben Sie die Produktionen an. + + Wie könnte man die Linksrekursionen entfernen? Geben Sie eine umgeformte EBNF Grammatik ohne Linksrekursionen an. Ersetzten Sie die Linksrekursionen dabei durch Iterationen. + + ```ebnf + Object = ident ":" "{" Props "}" ";". + Props = ident ":" Value | Props "," ident ":" Value . + Value = "’" text "’" | Value "+" "’" text "’" | ε . + ``` + + Beispielsätze: + ``` + alice : { name: ’Alice’, greeting: ’welcome’ + ’alice’ }; + bob: { name: ’Bob’, greeting: ’hello’ + ’to’ + ’bob’ }; + test: { noValue: , emptyValue: ’empty’, plusValue: + ’plus’ }; + ``` +] + +=== Task 1 + +- line 2: Props is left recursive +- line 3: Value is left recursive + +=== Task 2 + +```ebnf +Props = ident ":" Value { "," ident ":" Value } ";". +Value = (ε | "’" text "’") {"+" "’" text "’"}. +``` + +#figure( + image("task3.2.svg"), +) diff --git a/task3.2.excalidraw b/task3.2.excalidraw new file mode 100644 index 0000000..5e340d5 --- /dev/null +++ b/task3.2.excalidraw @@ -0,0 +1,1637 @@ +{ + "type": "excalidraw", + "version": 2, + "source": "https://excalidraw.com", + "elements": [ + { + "id": "ooTHOjvM-YpLBDzR09WfU", + "type": 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