Computation with Absolutely No Space Overhead Lane Hemaspaandra 1 - PowerPoint PPT Presentation

Outline Computation with Absolutely No Space Overhead Lane Hemaspaandra 1 Proshanto Mukherji 1 Till Tantau 2 1 Department of Computer Science University of Rochester 2 Fakult¨ at f¨ ur Elektrotechnik und Informatik Technical University of Berlin Developments in Language Theory Conference, 2003 Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Outline Outline The Model of Overhead-Free Computation 1 The Standard Model of Linear Space Our Model of Absolutely No Space Overhead The Power of Overhead-Free Computation 2 Palindromes Linear Languages Context-Free Languages with a Forbidden Subword Languages Complete for Polynomial Space Limitations of Overhead-Free Computation 3 Linear Space is Strictly More Powerful Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Outline Outline The Model of Overhead-Free Computation 1 The Standard Model of Linear Space Our Model of Absolutely No Space Overhead The Power of Overhead-Free Computation 2 Palindromes Linear Languages Context-Free Languages with a Forbidden Subword Languages Complete for Polynomial Space Limitations of Overhead-Free Computation 3 Linear Space is Strictly More Powerful Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Outline Outline The Model of Overhead-Free Computation 1 The Standard Model of Linear Space Our Model of Absolutely No Space Overhead The Power of Overhead-Free Computation 2 Palindromes Linear Languages Context-Free Languages with a Forbidden Subword Languages Complete for Polynomial Space Limitations of Overhead-Free Computation 3 Linear Space is Strictly More Powerful Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Outline The Model of Overhead-Free Computation 1 The Standard Model of Linear Space Our Model of Absolutely No Space Overhead The Power of Overhead-Free Computation 2 Palindromes Linear Languages Context-Free Languages with a Forbidden Subword Languages Complete for Polynomial Space Limitations of Overhead-Free Computation 3 Linear Space is Strictly More Powerful Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape 0 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Computation with Absolutely No Space Overhead The Standard Model of Linear Space 2004-04-19 The Model of Overhead-Free Computation tape 0 0 1 0 0 1 0 0 The Standard Model of Linear Space Characteristics Input fills fixed-size tape Input may be modified The Standard Model of Linear Space Tape alphabet is larger than input alphabet Turing machine 1. Point out that $ is a marker symbol. 2. Stress the larger tape alphabet.

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ 0 1 0 0 1 0 $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ 0 1 0 0 1 0 $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ $ 1 0 0 1 0 $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ $ 1 0 0 1 0 $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ $ 1 0 0 1 $ $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ $ $ $ $ $ $ $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary The Standard Model of Linear Space tape $ $ $ $ $ $ $ $ Characteristics Input fills fixed-size tape Input may be modified Tape alphabet is larger than input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Linear Space is a Powerful Model PSPACE -hard PSPACE NLINSPACE = CSL DLINSPACE CFL Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Computation with Absolutely No Space Overhead Linear Space is a Powerful Model 2004-04-19 PSPACE -hard The Model of Overhead-Free Computation PSPACE NLINSPACE = CSL The Standard Model of Linear Space DLINSPACE Linear Space is a Powerful Model CFL 1. Explain CSL. 2. Point out the connections to formal language theory.

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Outline The Model of Overhead-Free Computation 1 The Standard Model of Linear Space Our Model of Absolutely No Space Overhead The Power of Overhead-Free Computation 2 Palindromes Linear Languages Context-Free Languages with a Forbidden Subword Languages Complete for Polynomial Space Limitations of Overhead-Free Computation 3 Linear Space is Strictly More Powerful Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Our Model of “Absolutely No Space Overhead” tape 0 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet equals input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Our Model of “Absolutely No Space Overhead” tape 1 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet equals input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Our Model of “Absolutely No Space Overhead” tape 1 0 1 0 0 1 0 0 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet equals input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Our Model of “Absolutely No Space Overhead” tape 1 0 1 0 0 1 0 1 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet equals input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead

Models Power of the Model Standard Model Limitations of the Model Our Model Summary Our Model of “Absolutely No Space Overhead” tape 1 0 1 0 0 1 0 1 Characteristics Input fills fixed-size tape Input may be modified Tape alphabet equals input alphabet Turing machine Hemaspaandra, Mukherji, Tantau Computation with Absolutely No Space Overhead