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OP-11907Status unassessedAlgebra

Circuit size for path provenance over absorptive semirings

Circuit size for path provenance over absorptive semirings. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

MSC 16Y60 · SemiringsMSC 68P15 · Database theory

Editorial MSC2020 mapping of Circuit size for path provenance over absorptive semirings. https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume15/issue02/25081/DagRep.15.2.89/DagRep.15.2.89.pdf#page=17 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
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Problem statement

Let each edge of the complete nn-vertex graph carry a variable, and sum the products associated with simple paths from vertex 11 to vertex nn. Over semirings satisfying 1+x=11+x=1, what is the optimal arithmetic-circuit size for this path-provenance polynomial? The report gives an O(n3)O(n^3) upper bound and an Ω(n2)\Omega(n^2) lower bound.

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Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

References
  1. [1]Seminar 25081 problem-session contributors. Dagstuhl 25081 — Semirings in Database Theory (2025).; Circuit size for path provenance over absorptive semirings linkCC BY 4.0; attributed editorial adaptation of the named section authors.

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