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Lecture Theory of automata - Lecture 45

This chapter presents the following content: Turing machine, examples, DELETE subprogram, example, INSERT subprogram, example, whether the given string is generated by the given CFG (membership), example, parsing techniques, top down parsing, example. | Recap lecture 44 Decidability, whether a CFG generates certain string (emptiness), examples, whether a nonterminal is used in the derivation of some word (uselessness), examples, whether a CFL is finite (finiteness), example, whether the given string is generated by the given CFG (membership), example, parsing techniques, top down parsing, example Turing machine The mathematical models (FAs, TGs, PDAs) that have been discussed so far can decide whether a string is accepted or not by them i.e. these models are language identifiers. However, there are still some languages which can’t be accepted by them e.g. there does not exist any FA or TG or PDA accepting any non-CFLs. Alan Mathison Turing developed the machines called Turing machines, which accept some non-CFLs as well, in addition to CFLs. Turing machine Definition: A Turing machine (TM) consists of the following An alphabet of input letters. An input TAPE partitioned into cells, having infinite many locations in one . | Recap lecture 44 Decidability, whether a CFG generates certain string (emptiness), examples, whether a nonterminal is used in the derivation of some word (uselessness), examples, whether a CFL is finite (finiteness), example, whether the given string is generated by the given CFG (membership), example, parsing techniques, top down parsing, example Turing machine The mathematical models (FAs, TGs, PDAs) that have been discussed so far can decide whether a string is accepted or not by them i.e. these models are language identifiers. However, there are still some languages which can’t be accepted by them e.g. there does not exist any FA or TG or PDA accepting any non-CFLs. Alan Mathison Turing developed the machines called Turing machines, which accept some non-CFLs as well, in addition to CFLs. Turing machine Definition: A Turing machine (TM) consists of the following An alphabet of input letters. An input TAPE partitioned into cells, having infinite many locations in one direction. The input string is placed on the TAPE starting its first letter on the cell i, the rest of the TAPE is initially filled with blanks ( ’s). Turing machine continued A tape Head can read the contents of cell on the TAPE in one step. It can replace the character at any cell and can reposition itself to the next cell to the right or to the left of that it has just read. . . . a b a iv iii ii i TAPE Head Input TAPE Turing machine continued Initially the TAPE Head is at the cell i. The TAPE Head can’t move to the left of cell i. the location of the TAPE Head is denoted by . An alphabet of characters that can be printed on the TAPE by the TAPE Head. may include the letters of . Even the TAPE Head can print blank , which means to erase some character from the TAPE. Turing machine continued Finite set of states containing exactly one START state and some (may be none) HALT states that cause execution to terminate when the HALT states are entered. A program .