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## Erik Jonsson School of Engineering and Computer Science

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**Erik Jonsson School of Engineering**and Computer Science CS 4384– 001 Automata Theory http://www.utdallas.edu/~pervin Tuesday: Context-Free Languages Chapter Three – Review All Tuesday3-25-14 FEARLESS Engineering**A search of Albert Einstein's archived manuscripts last year**turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe. Einstein was attempting to make sense of Edwin Hubble's observation that the universe was expanding, but he made a mathematical error. When he discovered his mistake, he set aside the paper, which is now in a digital archive of his papers at the Hebrew University in Jerusalem. Waterford Institute of Technology physicist Cormac O'Raifeartaigh and colleagues found the paper while scouring the archive.**Because of this talk, there will be NO class Thursday, March**27th**Context-free Languages**Chapter Three**Other Simplifications**Useful variables and productions Left-recursion**Left-recursion**3-04-14**Pushdown Automata**Many similar definitions**PUMPING LEMMA**Context-Free**NOTE: CFLs are not closed under intersection (or**complement)!**Read and push a’s onto stack if any; read and ignore b’s**if any; read and match c’s with stack exactly.**Read and push a’s onto the stack; read b’s and match**them against the stack until empty; read any additional b’s and push them onto the stack; read and match c’s with stack exactly.**For each a read, non-deterministically push ONE or TWO a’s**on the stack; then match b’s read exactly with stack.