
Presburger arithmetic with threshold counting quantifiers is easy
We give a quantifier elimination procedures for the extension of Presbur...
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The Complexity of Bisimulation and Simulation on Finite Systems
In this paper the computational complexity of the (bi)simulation problem...
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A theory of finite structures
We develop a novel formal theory of finite structures, based on a view o...
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Definable isomorphism problem
We investigate the isomorphism problem in the setting of definable sets ...
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On the computational complexity of MSTD sets
We outline a general algorithm for verifying whether a subset of the int...
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Complexity of controlled bad sequences over finite sets of N^k
We provide lower and upper bounds for the length of controlled bad seque...
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The Bhargava greedoid as a Gaussian elimination greedoid
Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Pe...
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The theory of hereditarily bounded sets
We show that for any k∈ω, the structure (H_k,∈) of sets that are hereditarily of size at most k is decidable. We provide a transparent complete axiomatization of its theory, a quantifier elimination result, and tight bounds on its computational complexity. This stands in stark contrast to the structure V_ω=⋃_k H_k of hereditarily finite sets, which is well known to be biinterpretable with the standard model of arithmetic (ℕ,+,·).
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