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Tree Automata [article]

Ferenc Gécseg, Magnus Steinby
2015 arXiv   pre-print
This is a reissue of the book Tree Automata by F. G\'ecseg and M. Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest.  ...  Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references.  ...  The grammar G is ambiguous if some word w in L(G) has two different leftmost derivations from a 0 . Otherwise G is unambiguous.  ... 
arXiv:1509.06233v1 fatcat:ejhy6a7h2fcatcdfxv3hylresu

The monoidal structure of Turing machines

2013 Mathematical Structures in Computer Science  
Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra.  ...  On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular  ...  Isomorphism classes of C-automata are called circuits, and Circ(C) is the quotient of Aut C by this isomorphism.  ... 
doi:10.1017/s0960129512000096 fatcat:okauutp5ije43huy42haza7vga

Chasing Individuation: Mathematical Description of Physical Systems [article]

Federico Zalamea
2016 arXiv   pre-print
The question becomes then to understand the precise articulation between these two roles.  ...  Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity  ...  Acknowledgments The four years of research culminating with this dissertation were almost entirely  ... 
arXiv:1612.02959v1 fatcat:a2qsxtgt4bc2dnb7nzvdlcatna

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
= elliptic curves can be obtained as quotients of the complex plane and any genus g > 1 surface can be obtained as quotients of the unit disk.  ...  Linear programming Given two vectors c ∈ R m and b ∈ R n , and a n × m matrix A, a linear program is the variational problem on R m to maximize f (x) = c • x subject to the linear constraints Ax ≤ b and  ...  There are two basic operations: the addition A + B of two sets is defined as the set of all points which are in exactly one of the sets.  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

Cartesian closed bicategories: type theory and coherence [article]

Philip Saville
2020 arXiv   pre-print
For the second, which is the central preoccupation of this thesis, the proof strategy has two parts: the construction of a type theory, and the proof that it satisfies a form of normalisation I call "local  ...  I show that there is at most one 2-cell between any parallel pair of 1-cells in the free cartesian closed bicategory on a set and hence---in terms of the difficulty of calculating---bring the data of cartesian  ...  Every multicategory L defines a category L by restricting to linear morphisms.  ... 
arXiv:2007.00624v1 fatcat:lz5ssbkjdjamrdojhml7q3k65y