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lfa:lab03-dfa-regexp [2021/09/28 12:31] pdmatei |
lfa:lab03-dfa-regexp [2021/10/16 18:57] (current) pdmatei |
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| - | ===== 4.2. Regex implementation ===== | + | ===== 4.2. Writing Regular Expressions ===== |
| + | |||
| + | **4.2.1.** Write a regular expression for the language of arithmetic expressions containing +, * and numbers. | ||
| + | **Hint:** you can abbreviate $ 0 \cup 1 \cup ... \cup 9 $ by $ [0-9] $ | ||
| + | |||
| + | **4.2.2.** Write a regular expression for $ L = \{ \omega \text{ in } \text{{0,1}} ^* \text{ | EVERY sequence of two or more consecutive zeros appears before ANY sequence of two or more consecutive ones} \} $ | ||
| + | |||
| + | **4.2.3.** Write a DFA for $ L(( 10 \cup 0) ^* ( 1 \cup \epsilon )) $ | ||
| + | |||
| + | **4.2.4.** Write a regular expression which generates the accepted language of A: | ||
| + | |||
| + | {{:lfa:graf1.png?200|}} | ||
| + | |||
| + | **4.2.5.** Simplify the regular expression you found. | ||
| + | |||
| + | **4.2.6.** Describe as precisely as possible the language generated by $math[(1 \cup 1(01^*0)1)^*] | ||
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| + | |||
| + | ===== 4.3. Regex implementation (Python) ===== | ||
| ==== Inheritance and isinstance ==== | ==== Inheritance and isinstance ==== | ||
| Line 78: | Line 96: | ||
| </code> | </code> | ||
| + | **4.3.1.** Write a class hierarchy for Regular Expressions, and add the ''__str__'' function for each of them. Implement a constructor which reads a Regular Expression in **Prenex form**, from a string. The prenex form is illustrated below via examples: | ||
| + | <code Python> | ||
| + | # a* | ||
| + | s = "STAR a" | ||
| - | ==== Classes in Python ==== | + | # ab |
| + | s = "CONCAT a b" | ||
| + | # a U b | ||
| + | s = "UNION a b" | ||
| - | ===== 4.3. Writing Regular Expressions ===== | + | # (a U b)*c* |
| + | s = "CONCAT STAR UNION a b STAR c" | ||
| + | </code> | ||
| - | \\ | + | Hints: |
| - | **4.3.1.** Write a regular expression for the language of arithmetic expressions containing +, * and numbers. | + | * To properly read a regular expression, you need a **state** of the parsing process, as well as information about what was parsed. What kind of data-structure is necessary for this step? This data-structure will be widely-used later, when we discuss Push-down Automata. |
| - | **Hint:** you can abbreviate $ 0 \cup 1 \cup ... \cup 9 $ by $ [0-9] $ | + | |
| - | **4.3.2.** Write a regular expression for $ L = \{ \omega \text{ in } \text{{0,1}} ^* \text{ | every sequence of consecutive zeros appears before ANY sequence of consecutive ones} \} $ | + | <hidden More hints> |
| + | The following table illustrates the string parsing and stack contents (ADT style) for the last example. | ||
| + | ^ String contents ^ Stack ^ | ||
| + | | ''CONCAT STAR UNION a b STAR c'' | Void | | ||
| + | | ''STAR UNION a b STAR c'' | Push(Concat(?,?),Void) | | ||
| + | | ''UNION a b STAR c'' | Push(Star(?), Push(Concat(?,?),Void)) | | ||
| + | | ''a b STAR c'' | Push(Union(?,?), Push(Star(?), Push(Concat(?,?),Void))) | | ||
| + | | ''b STAR c'' | Push(a, Push(Union(?,?), Push(Star(?), Push(Concat(?,?),Void)))) | | ||
| + | | ''b STAR c'' | Push(Union(a,?), Push(Star(?), Push(Concat(?,?),Void))) | | ||
| + | | ''STAR c'' | Push(b, Push(Union(a,?), Push(Star(?), Push(Concat(?,?),Void)))) | | ||
| + | | ''STAR c'' | Push(Union(a,b), Push(Star(?), Push(Concat(?,?),Void))) | | ||
| + | | ''STAR c'' | Push(Star(Union(a,b)), Push(Concat(?,?),Void))) | | ||
| + | | ''STAR c'' | Push(Concat(Star(Union(a,b)),?),Void))) | | ||
| + | | ''c'' | Push(Star(?),Push(Concat(Star(Union(a,b)),?),Void)))) | | ||
| + | | | Push(c, Push(Star(?),Push(Concat(Star(Union(a,b)),?),Void))))) | | ||
| + | | | Push(Star(c),Push(Concat(Star(Union(a,b)),?),Void)))) | | ||
| + | | | Push(Concat(Star(Union(a,b)),Star(c)),Void)))) | | ||
| - | **4.3.3.** Write a DFA for $ L(( 10 \cup 0) ^* ( 1 \cup \epsilon )) $ | + | The string has been consumed and the stack holds one expression, thus the result is: ''Concat(Star(Union(a,b)),Star(c))''. |
| - | **4.3.4.** Write a regular expression which generates the accepted language of A: | + | </hidden> |
| - | {{:lfa:graf1.png?200|}} | + | ===== 4.4. Regex implementation (Haskell) ===== |
| - | **4.3.5.** Simplify the regular expression you found. | + | **4.4.1.** Implement the ADT ''Regex''. |
| - | **4.3.6.** Describe as precisely as possible the language generated by $math[(1 \cup 1(01^*0)1)^*] | + | **4.4.2.** Enrol the type in class ''Show''. |
| + | **4.4.3.** Write a function which takes a string containing a regex in prenex form (see the Python exercises) and returns a ''Regex''. ***Hint:** use two mutually recursive functions and see the hints regarding the stack from the Python implementation section. | ||