FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3040249201> ?p ?o ?g. }

• W3040249201 abstract "One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $mathbf{P}notsubseteqmathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested to approach this problem by proving that depth complexity behaves expected with respect to the composition of functions $fdiamond g$. They showed that the validity of this conjecture would imply that $mathbf{P}notsubseteqmathbf{NC}^1$. Several works have made progress toward resolving this conjecture by proving special cases. In particular, these works proved the KRW conjecture for every outer function $f$, but only for few inner functions $g$. Thus, it is an important challenge to prove the KRW conjecture for a wider range of inner functions. In this work, we extend significantly the range of inner functions that can be handled. First, we consider the $textit{monotone}$ version of the KRW conjecture. We prove it for every monotone inner function $g$ whose depth complexity can be lower bounded via a query-to-communication lifting theorem. This allows us to handle several new and well-studied functions such as the $stextbf{-}t$-connectivity, clique, and generation functions. In order to carry this progress back to the $textit{non-monotone}$ setting, we introduce a new notion of $textit{semi-monotone}$ composition, which combines the non-monotone complexity of the outer function $f$ with the monotone complexity of the inner function $g$. In this setting, we prove the KRW conjecture for a similar selection of inner functions $g$, but only for a specific choice of the outer function $f$." @default.
• W3040249201 created "2020-07-10" @default.
• W3040249201 creator A5003318200 @default.
• W3040249201 creator A5003633660 @default.
• W3040249201 creator A5021914150 @default.
• W3040249201 creator A5057666042 @default.
• W3040249201 creator A5071686980 @default.
• W3040249201 date "2020-07-06" @default.
• W3040249201 modified "2023-10-16" @default.
• W3040249201 title "KRW Composition Theorems via Lifting" @default.
• W3040249201 cites W127278483 @default.
• W3040249201 cites W1671393514 @default.
• W3040249201 cites W175482385 @default.
• W3040249201 cites W1898488645 @default.
• W3040249201 cites W1966278576 @default.
• W3040249201 cites W1968655942 @default.
• W3040249201 cites W1991702990 @default.
• W3040249201 cites W1995365759 @default.
• W3040249201 cites W2003104918 @default.
• W3040249201 cites W2004004688 @default.
• W3040249201 cites W2005223599 @default.
• W3040249201 cites W2020513176 @default.
• W3040249201 cites W2026987631 @default.
• W3040249201 cites W2041210515 @default.
• W3040249201 cites W2049016755 @default.
• W3040249201 cites W2050688507 @default.
• W3040249201 cites W2061739322 @default.
• W3040249201 cites W2077740213 @default.
• W3040249201 cites W2093396771 @default.
• W3040249201 cites W2129059686 @default.
• W3040249201 cites W2141585995 @default.
• W3040249201 cites W2154150949 @default.
• W3040249201 cites W2220094226 @default.
• W3040249201 cites W2340787257 @default.
• W3040249201 cites W2536688806 @default.
• W3040249201 cites W2563018125 @default.
• W3040249201 cites W2565821653 @default.
• W3040249201 cites W2588984325 @default.
• W3040249201 cites W2624730843 @default.
• W3040249201 cites W2741968539 @default.
• W3040249201 cites W2768048099 @default.
• W3040249201 cites W2768857456 @default.
• W3040249201 cites W2787163834 @default.
• W3040249201 cites W2809402609 @default.
• W3040249201 cites W2897781990 @default.
• W3040249201 cites W2950340987 @default.
• W3040249201 cites W2963260788 @default.
• W3040249201 cites W2963815293 @default.
• W3040249201 cites W3004119281 @default.
• W3040249201 cites W3022335368 @default.
• W3040249201 cites W3030925942 @default.
• W3040249201 cites W3033309051 @default.
• W3040249201 cites W3130516212 @default.
• W3040249201 cites W3137706500 @default.
• W3040249201 cites W42251193 @default.
• W3040249201 cites W2593413964 @default.
• W3040249201 hasPublicationYear "2020" @default.
• W3040249201 type Work @default.
• W3040249201 sameAs 3040249201 @default.
• W3040249201 citedByCount "0" @default.
• W3040249201 crossrefType "posted-content" @default.
• W3040249201 hasAuthorship W3040249201A5003318200 @default.
• W3040249201 hasAuthorship W3040249201A5003633660 @default.
• W3040249201 hasAuthorship W3040249201A5021914150 @default.
• W3040249201 hasAuthorship W3040249201A5057666042 @default.
• W3040249201 hasAuthorship W3040249201A5071686980 @default.
• W3040249201 hasConcept C10138342 @default.
• W3040249201 hasConcept C114614502 @default.
• W3040249201 hasConcept C118615104 @default.
• W3040249201 hasConcept C134306372 @default.
• W3040249201 hasConcept C138885662 @default.
• W3040249201 hasConcept C14036430 @default.
• W3040249201 hasConcept C159985019 @default.
• W3040249201 hasConcept C162324750 @default.
• W3040249201 hasConcept C182306322 @default.
• W3040249201 hasConcept C192562407 @default.
• W3040249201 hasConcept C204323151 @default.
• W3040249201 hasConcept C2524010 @default.
• W3040249201 hasConcept C2777035058 @default.
• W3040249201 hasConcept C2780990831 @default.
• W3040249201 hasConcept C2834757 @default.
• W3040249201 hasConcept C33923547 @default.
• W3040249201 hasConcept C34388435 @default.
• W3040249201 hasConcept C39927690 @default.
• W3040249201 hasConcept C40231798 @default.
• W3040249201 hasConcept C41895202 @default.
• W3040249201 hasConcept C78458016 @default.
• W3040249201 hasConcept C86803240 @default.
• W3040249201 hasConceptScore W3040249201C10138342 @default.
• W3040249201 hasConceptScore W3040249201C114614502 @default.
• W3040249201 hasConceptScore W3040249201C118615104 @default.
• W3040249201 hasConceptScore W3040249201C134306372 @default.
• W3040249201 hasConceptScore W3040249201C138885662 @default.
• W3040249201 hasConceptScore W3040249201C14036430 @default.
• W3040249201 hasConceptScore W3040249201C159985019 @default.
• W3040249201 hasConceptScore W3040249201C162324750 @default.
• W3040249201 hasConceptScore W3040249201C182306322 @default.
• W3040249201 hasConceptScore W3040249201C192562407 @default.
• W3040249201 hasConceptScore W3040249201C204323151 @default.
• W3040249201 hasConceptScore W3040249201C2524010 @default.

• next