$$\mathbb {N}$$ -Memory Automata over the Alphabet $$\mathbb {N}$$

Brütsch, Benedikt; Landwehr, Patrick; Thomas, Wolfgang

doi:10.1007/978-3-319-53733-7_6

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…The model of RA Q can be seen as an extension of RA with data variables and linear arithmetics on them. There is also another RA model over the alphabet N with order and successor relations in guards, but no arithmetic on the input word [39].…”

Section: Related Workmentioning

confidence: 99%

Register automata with linear arithmetic

Chen

Lengál

Tan

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA Q ). It reads a sequence of rational numbers and outputs another rational number. RA Q is an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RA Q model allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits.The main feature of RA Q is that despite the use of linear arithmetic, the so-called invariant problem-a generalization of the standard non-emptiness problem-is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RA Q , commutativity and equivalence are polynomial-time inter-reducible with the invariant problem. * Though normally called registers, for reasons that will be apparent later, we will refer to them as variables in this paper. 978-1-5090-3018-7/17/$31.00 c 2017 IEEE § A guard is non-strict if it does not contain negations, i.e., it is a positive Boolean combination of inequalities z z ′ .

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Section: Related Workmentioning

confidence: 99%

Register automata with linear arithmetic

Chen

Lengál

Tan

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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$$\textsc {Reach}$$ on Register Automata via History Independence

Dierl

Howar

2022

Tests and Proofs

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Solving Infinite Games in the Baire Space

Brütsch

Thomas

2022

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Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space ωω. We consider such games defined by a natural kind of parity automata over the alphabet ℕ, called ℕ-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical Büchi-Landweber Theorem (for finite-state games in the Cantor space 2ω) holds again for the present games: A game defined by a deterministic parity ℕ-MSO-automaton is determined, the winner can be computed, and an ℕ-MSO-transducer realizing a winning strategy for the winner can be constructed.

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$$\mathbb {N}$$ -Memory Automata over the Alphabet $$\mathbb {N}$$

Cited by 3 publications

References 12 publications

Register automata with linear arithmetic

Register automata with linear arithmetic

$$\textsc {Reach}$$ on Register Automata via History Independence

Solving Infinite Games in the Baire Space

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