*Pierluigi Frisco*

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199542864
- eISBN:
- 9780191715679
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199542864.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Biology

How could we use living cells to perform computation? Would our definition of computation change as a consequence of this? Could such a cell-computer outperform digital computers? These are some of ...
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How could we use living cells to perform computation? Would our definition of computation change as a consequence of this? Could such a cell-computer outperform digital computers? These are some of the questions that the study of Membrane Computing tries to answer and are at the base of what is treated by this monograph. Descriptional and computational complexity of models in Membrane Computing are the two lines of research on which is the focus here. In this context this book reports the results of only some of the models present in this framework. The models considered here represent a very relevant part of all the models introduced so far in the study of Membrane Computing. They are in between the most studied models in the field and they cover a broad range of features (using symbol objects or string objects, based only on communications, inspired by intra- and intercellular processes, having or not having a tree as underlying structure, etc.) that gives a grasp of the enormous flexibility of this framework. Links with biology and Petri nets are constant through this book. This book aims also to inspire research. This book gives suggestions for research of various levels of difficulty and this book clearly indicates their importance and the relevance of the possible outcomes. Readers new to this field of research will find the provided examples particularly useful in the understanding of the treated topics.Less

How could we use living cells to perform computation? Would our definition of *computation* change as a consequence of this? Could such a cell-computer outperform digital computers? These are some of the questions that the study of *Membrane Computing* tries to answer and are at the base of what is treated by this monograph. Descriptional and computational complexity of models in Membrane Computing are the two lines of research on which is the focus here. In this context this book reports the results of only *some* of the models present in this framework. The models considered here represent a very relevant part of all the models introduced so far in the study of Membrane Computing. They are in between the most studied models in the field and they cover a broad range of features (using symbol objects or string objects, based only on communications, inspired by intra- and intercellular processes, having or not having a tree as underlying structure, etc.) that gives a grasp of the enormous flexibility of this framework. Links with biology and Petri nets are constant through this book. This book aims also to inspire research. This book gives suggestions for research of various levels of difficulty and this book clearly indicates their importance and the relevance of the possible outcomes. Readers new to this field of research will find the provided examples particularly useful in the understanding of the treated topics.

*Cristopher Moore and Stephan Mertens*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199233212
- eISBN:
- 9780191775079
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233212.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. However, this beauty is often ...
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Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. However, this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results such as interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. It starts with a lucid explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. It then leads the reader through the complexity of mazes and games; optimisation in theory and practice; randomised algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, it uses a minimum of formalism, providing explanations that are both deep and accessible.Less

Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. However, this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results such as interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. It starts with a lucid explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. It then leads the reader through the complexity of mazes and games; optimisation in theory and practice; randomised algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, it uses a minimum of formalism, providing explanations that are both deep and accessible.