Book ChapterDOI
Finite automata over structures
Aniruddh Gandhi,Bakhadyr Khoussainov,Jiamou Liu +2 more
- pp 373-384
TLDR
In this paper, a finite automata model for performing computations over an arbitrary structure is introduced, where the automaton processes sequences of elements in the structure and makes state transitions.Abstract:
We introduce a finite automata model for performing computations over an arbitrary structure $\mathcal S$ . The automaton processes sequences of elements in $\mathcal S$ . While processing the sequence, the automaton tests atomic relations, performs atomic operations of the structure $\mathcal S$ , and makes state transitions. In this setting, we study several problems such as closure properties, validation problem and emptiness problems. We investigate the dependence of deciding these problems on the underlying structures and the number of registers of our model of automata. Our investigation demonstrates that some of these properties are related to the existential first order fragments of the underlying structures.read more
Citations
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Book ChapterDOI
A Survey on Analog Models of Computation.
Olivier Bournez,Amaury Pouly +1 more
TL;DR: A survey on analog models of computations, which considers both approaches, often intertwined, with a point of view mostly oriented by computation theory.
Journal ArticleDOI
Generalized finite automata over real and complex numbers
Klaus Meer,Ameen Naif +1 more
TL;DR: This paper proves several structural results about sets accepted by such automata, and analyzes decidability as well as complexity of several classical questions about automata in the new framework.
Journal ArticleDOI
Recognizable series on graphs and hypergraphs
TL;DR: A computational model that generically associates a tensor network to a graph or a hypergraph and then computes a value by generalized tensor contractions directed by its hyperedges, which generalizes the notion of recognizable series on strings and trees.
Book ChapterDOI
Generalized Finite Automata over Real and Complex Numbers
Klaus Meer,Ameen Naif +1 more
TL;DR: This work introduced and studied a generalized model of finite automata able to work over arbitrary structures and identified studying such automata over partciular structures such as real and algebraically closed fields as one relevant area of research for this model.
Book ChapterDOI
Periodic Generalized Automata over the Reals
Klaus Meer,Ameen Naif +1 more
TL;DR: A generalized model of finite automata able to work over arbitrary structures but has an additional ability to perform in a restricted way operations attached to the structure under consideration.
References
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Journal ArticleDOI
On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
Book ChapterDOI
Disjunctive Tautologies as Synchronisation Schemes
Vincent Danos,Jean-Louis Krivine +1 more
TL;DR: In the ambient logic of classical second order propositional calculus, the specification problem for a family of excluded middle like tautologies is solved and these are shown to be realized by sequential simulations of specific communication schemes for which they provide a safe typing mechanism.
Book ChapterDOI
Computational Adequacy in an Elementary Topos
TL;DR: It is proved that computational adequacy holds if and only if the topos is 1-consistent (i.e. its internal logic validates only true Σ\(^{\rm 0}_{\rm 1}\)-sentences).
Journal ArticleDOI
Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines
TL;DR: The main results of this paper show that the same notions of computability can be realized within the highly restricted monogenic formal systems called by Post the "Tag" systems, and within a peculiarly restricted variant of Turing machine which has two tapes, but can neither write on nor erase these tapes.