4 papers · 1 filter
Partial Path Interception in Derivation DAGs: Exact Reliability Laws and a Sharp Complexity Dichotomy
Jianfeng Xu
We introduce partial path interception on derivation DAGs (directed acyclic graphs), a combinatorial optimization problem arising from proof-valid caching: stored objects must be l…
Closure-Preserving Rate-Distortion for Reversible Logging
Jianfeng Xu
We study semantic compression of reversible-execution evidence for rollback reasoning. A run is a finite fact base; rollback semantics are modeled by a monotone closure operator in…
Rate-Distortion Theory for Deductive Sources under Closure Fidelity
Jianfeng Xu
We study lossy compression of a finite statement source generated in a fixed deductive environment. The source symbols are statements in a knowledge base endowed with a shared proo…
Semantic Rate-Distortion Theory: Deductive Compression and Closure Fidelity
Jianfeng Xu
Shannon's rate-distortion theory treats source symbols as unstructured labels. When the source is a knowledge base equipped with a logical proof system, a natural fidelity criterio…