Formal Languages Automata And Numeration Systems 2
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Formal Languages, Automata and Numeration Systems 2
The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.
Formal Languages, Automata and Numeration Systems 1
Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.
Solving Transport Problems
Solving Transport Problems establishes fundamental points and good practice in resolving matters regarding green transportation. This is to prompt further research in conveyance issues by providing readers with new knowledge and grounds for integrated models and solution methods. Focusing on green transportation, this book covers various sub-topics and thus consists of diverse content. Traditionally, academia and transport practitioners have mainly concentrated on efficient fleet management to achieve economic benefits and better-quality service. More recently, due to growing public environmental concerns and the industry understanding of the issue, the academic community has started to address environmental issues. The studies of green transportation compiled in this book have identified certain areas of interest, such as references, viewpoints, algorithms and ideas. Solving Transport Problems is for researchers, environmental decision-makers and other concerned parties, to start discussion on developing optimized technology and alternative fuel-based integrated models for environmentally cleaner transport systems.