main results
means
formal power series
existence
978-1-4612-6264-0
arithmetization
analysis
main emphasis
instances
theoretical computer scientists
lead
https://doi.org/10.1007/978-1-4612-6264-0
book
https://scigraph.springernature.com/explorer/license/
variables
1978-01-01
2022-08-04T17:13
scientists
readers
estimation
algebra
extent
theory
specific results
books
work
group
false
background
language theory
mathematical formalism
formal language theory
emphasis
Schutzenberger
powerful tool
unfortunate effect
automata
results
free group
effect
tool
series
1978
This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.
computer scientists
formalism
monograph
aspects
point
978-1-4612-6266-4
Automata-Theoretic Aspects of Formal Power Series
fact
lack
connection
power series
doi
10.1007/978-1-4612-6264-0
Springer Nature
Soittola
Matti
Pure Mathematics
Salomaa
Arto
pub.1046944411
dimensions_id
Springer Nature - SN SciGraph project
Mathematical Sciences
Department of Mathematics, University of Turku, 20500, Turku 50, Finland
Department of Mathematics, University of Turku, 20500, Turku 50, Finland