3-SAT → Elastic-degenerate string inequivalence Complexity open
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Why this question matters
The question concerns the cost of comparing compact representations of uncertain strings.
General regular-expression inequivalence does not immediately settle this finite, non-nested representation of string languages.
The reduction to construct
A source instance is an explicitly encoded Boolean formula with at most three literals per clause. Its outputs are satisfying Boolean assignments, or NO-SOLUTION when the formula is unsatisfiable.
Each target string is a sequence of finite sets of explicit words; concatenation defines its finite language. Find a word in the symmetric difference of the two languages, or report that the languages are equal. Nested language expressions are not allowed.
Construct deterministic polynomial-time maps F and G: F sends every legal source instance to a legal target instance, and G(x,y) is a valid source output for every valid output y of F(x). Preserve the stated threshold, domain and promises. The requested complexity conclusion is NP-hardness for the stated target problem.
Flattening unions can cause exponential growth, so a valid reduction must retain a polynomial explicit representation.
What a complete answer must include
Give explicit construction and recovery algorithms, a general proof for every legal input and every valid target output, and polynomial runtime and encoding-size bounds. Specify finite output encodings and handle NO-SOLUTION outputs when applicable. Tests compare recovered source outputs with independent source solutions.
References
Literature checked 2026-09-16. This summarizes the archived literature search on the date above. Unpublished, unindexed and overlooked work remains outside coverage; no new novelty assessment was performed.