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Lecture Theory of Automata: Lesson 41

Lecture Theory of Automata: Lesson 41. The main topics covered in this chapter include: recap of PDA in conversion form, example of PDA in conversion form, joints of the machine, new pictorial representation of PDA in conversion form, summary table, row sequence, row language, . | Recap lecture 40 Recap of example of PDA corresponding to CFG CFG corresponding to PDA. Theorem HERE state Definition of Conversion form different situations of PDA to be converted into conversion form 1 Conversion form of PDA Definition A PDA is in conversion form if it fulfills the following conditions 1. There is only one ACCEPT state. 2. There are no REJECT states. 3. Every READ or HERE is followed immediately by a POP i.e. every edge leading out of any READ or HERE state goes directly into a POP state. 2 CFG corresponding to PDA 4. No two POPs exist in a row on the same path without a READ or HERE between them whether or not there are any intervening PUSH states i.e. the POP states must be separated by READs or HEREs . 5. All branching deterministic or nondeterministic occurs at READ or HERE states none at POP states and every edge has only one label. 3 CFG corresponding to PDA 6. Even before we get to START a bottom of STACK symbol is placed on the STACK. If this symbol is ever popped in the processing it must be replaced immediately. The STACK is never popped beneath this symbol. Right before entering ACCEPT this symbol is popped out and left. 4 CFG corresponding to PDA 7. The PDA must begin with the sequence START POP PUSH HERE 8. The entire input string must be read before the machine can accept the word. 5 Example Consider the following PDA accepting the language a2nbn n 1 2 3 ST RD1 b POP1 a POP2 a RD2 b a PUSH a AT POP3 Which may be converted to 6 PUSH POP4 ST RD1 b POP1 a HERE POP2 a a a b RD 2 POP5 POP6 a AT POP3 PUSH a PUSH PUSH a PUSH a The above PDA accepts exactly the same language 7 Note It may be noted that any PDA which is conversion form can be considered to be the collection of path segments where each path segment is of the following form FROM TO READ POP PUSH START READ ONE or Exactly Any or READ or HERE no input one string or HERE or AT letter STACK onto the character 8 STACK Note continued START READ HERE and ACCEPT states are called the