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Title: Adventures in Monotone Complexity and TFNP
Separations: We introduce a monotone variant of Xor-Sat and show it has exponential monotone circuit complexity. Since Xor-Sat is in NC^2, this improves qualitatively on the monotone vs. non-monotone separation of Tardos (1988). We also show that monotone span programs over R can be exponentially more powerful than over finite fields. These results can be interpreted as separating subclasses of TFNP in communication complexity. Characterizations: We show that the communication (resp. query) analogue of PPA (subclass of TFNP) captures span programs over F_2 (resp. Nullstellensatz degree over F_2). Previously, it was known that communication FP captures formulas (Karchmer - Wigderson, 1988) and that communication PLS captures circuits (Razborov, 1995). Characterizations: We show that the communication (resp. query) analogue of PPA (subclass of TFNP) captures span programs over F_2 (resp. Nullstellensatz degree over F_2). Previously, it was known that communication FP captures formulas (Karchmer-Wigderson, 1988) and that communication PLS captures circuits (Razborov, 1995).  more » « less
Award ID(s):
1733808 1741137
NSF-PAR ID:
10112897
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Innovations in Theoretical Computer Science (ITCS 2019)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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