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Unconditional Proofs of Quantumness Between Small-Space Machines Cover

Unconditional Proofs of Quantumness Between Small-Space Machines

By: A. C. Cem Say and  M. Utkan Gezer  
Open Access
|Feb 2025

Figures & Tables

Figure 1.

A verifier V for a language recognized by 2DFA(2) M.
A verifier V for a language recognized by 2DFA(2) M.

Figure 2.

A prover that simulates N1 on its input and reports its head readings in each round.
A prover that simulates N1 on its input and reports its head readings in each round.

Figure 3.

A verifier based on a DS-FK problem (PAD(L), 

), where L ∈ ℒ(2DFA(2s)).
A verifier based on a DS-FK problem (PAD(L), ), where L ∈ ℒ(2DFA(2s)).

Figure 4.

A quantum prover based on (PAD(L), 

), where L ∈ BQTISP∗(2kn, s(n)) ∩ ℒ(2DFA(2s)).
A quantum prover based on (PAD(L), ), where L ∈ BQTISP∗(2kn, s(n)) ∩ ℒ(2DFA(2s)).

Figure 5.

A verifier V based on (PAD(SQUARE), PAD(SUBSQUARE)).
A verifier V based on (PAD(SQUARE), PAD(SUBSQUARE)).

Figure 6.

A quantum prover based on (PAD(SQUARE), PAD(SUBSQUARE)).
A quantum prover based on (PAD(SQUARE), PAD(SUBSQUARE)).

Some languages recognized in 2O(n) time by 2QCFAs_

LanguageDescription
PAL{ ww = wR }
TWIN{ w#ww ∈ { a, b } }
MULT{ x#y#z | x, y, z are natural numbers in binary notation and xy = z }
SQUARE{ aibi2i > 0 }
POWER{ aib2ii > 0 }
any “polynomial language”A polynomial language [27] is defined as {a1n1aknkb1p1(n1,,nk)brpr(n1,,nk)|pi(ni,,nk)0}, \{a_1^{{n_1}} \ldots a_k^{{n_k}}b_1^{{p_1}({n_1}, \ldots,{n_k})} \ldots b_r^{{p_r}({n_1}, \ldots,{n_k})}|{p_i}({n_i}, \ldots,{n_k}) \ge 0\}, , where a1, …, ak, b1, …, br are distinct symbols, and each pi is a polynomial with integer coefficients.
WGthe word problem for G, where G is any finitely generated virtually free group
DOI: https://doi.org/10.2478/qic-2025-0002 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
Language: English
Page range: 36 - 56
Submitted on: Nov 24, 2024
Accepted on: Jan 21, 2025
Published on: Feb 15, 2025
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2025 A. C. Cem Say, M. Utkan Gezer, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.