Pseudo-Deterministic Query Complexity of Search Problems
We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we show that the deterministic query complexity of total search problems is at most the third power of its...
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| Vydáno v: | Computational complexity Ročník 34; číslo 2; s. 20 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.12.2025
Springer Nature B.V |
| Témata: | |
| ISSN: | 1016-3328, 1420-8954 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we show that the deterministic query complexity of total search problems is at most the third power of its pseudo-deterministic query complexity. Previously, a fourth-power relation was shown by Goldreich, Goldwasser and Ron (ITCS'13). Using our proof along with a decision-tree manipulation technique, we give a simple and self-contained proof that the
SearchCNF
problem on random
k
-CNF has pseudo-deterministic query complexity
Ω
(
n
1
/
3
)
; a lower bound of
Ω
(
n
)
is known, due to Goldwasser, Impagliazzo, Pitassi, and Santhanam (CCC'21), but via a significantly more complex proof.
We improve the known separation between pseudo-deterministic and randomized decision tree size for total search problems in two ways: (1) We exhibit an
exp
(
Ω
~
(
n
1
/
4
)
)
separation for the
SearchCNF
relation for random
k
-CNFs. This seems to be the first exponential lower bound on the pseudo-deterministic size complexity of
SearchCNF
associated with random
k
-CNFs. (2) We exhibit an
exp
(
Ω
(
n
)
)
separation for the
ApproxHW
relation. The previous best known separation for any relation was
exp
(
Ω
(
n
1
/
2
)
)
.
We also separate pseudo-determinism from randomness in
AND
and
CONJ
decision trees, and determinism from pseudo-determinism in
Parity
decision trees.
Finally, for a hypercube colouring problem, that was introduced by Goldwasswer et al. to analyze the pseudo-deterministic complexity of a complete problem in
TFNPdt
, we prove that either the
monotone
block-sensitivity or the
anti-monotone
block sensitivity is
Ω
(
n
1
/
3
)
; Goldwasser et al. showed an
Ω
(
n
1
/
2
)
bound for
general
block-sensitivity. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1016-3328 1420-8954 |
| DOI: | 10.1007/s00037-025-00266-7 |