Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata

We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential t...

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Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Bojanczyk, Mikolaj, Klin, Bartek, Moerman, Joshua
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Automata
Complexity theory
Computer science
Orbits
Registers
Space vehicles
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Abstract We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing.
AbstractList We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing.
Author Klin, Bartek
Moerman, Joshua
Bojanczyk, Mikolaj
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  surname: Bojanczyk
  fullname: Bojanczyk, Mikolaj
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  organization: University of Warsaw
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  givenname: Bartek
  surname: Klin
  fullname: Klin, Bartek
  email: klin@mimuw.edu.pl
  organization: University of Warsaw
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  givenname: Joshua
  surname: Moerman
  fullname: Moerman, Joshua
  email: joshua@cs.rwth-aachen.de
  organization: RWTH Aachen
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Snippet We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register...
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SubjectTerms Automata
Complexity theory
Computer science
Orbits
Registers
Space vehicles
Title Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
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