
Deciding the Computability of Regular Functions over Infinite Words
The class of regular functions from infinite words to infinite words is ...
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A Galois connection between Turing jumps and limits
Limit computable functions can be characterized by Turing jumps on the i...
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Quantitative continuity and computable analysis in Coq
We give a number of formal proofs of theorems from the field of computab...
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Function Naming in Stripped Binaries Using Neural Networks
In this paper we investigate the problem of automatically naming pieces ...
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Infinite and Biinfinite Words with Decidable Monadic Theories
We study word structures of the form (D,<,P) where D is either N or Z, <...
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From Functional Nondeterministic Transducers to Deterministic TwoTape Automata
The question whether P = NP revolves around the discrepancy between acti...
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On the Computability of AIXI
How could we solve the machine learning and the artificial intelligence ...
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On Computability of Data Word Functions Defined by Transducers
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omegawords). The notion of computability is defined through Turing machines with infinite inputs which can produce the corresponding infinite outputs in the limit. We use nondeterministic transducers equipped with registers, an extension of register automata with outputs, to specify functions. Such transducers may not define functions but more generally relations of data omegawords, and we show that it is PSpacecomplete to test whether a given transducer defines a function. Then, given a function defined by some register transducer, we show that it is decidable (and again, PSpacecomplete) whether such function is computable. As for the known finite alphabet case, we show that computability and continuity coincide for functions defined by register transducers, and show how to decide continuity. We also define a subclass for which those problems are solvable in polynomial time.
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