Computer Science (CS43–CS87)

7 operators covering computational complexity, information theory, and parallelism. These operators are used by the Zeq platform for entropy measurement, complexity analysis, and performance optimisation.

CS43 — Sorting / FFT Complexity

T(n) = O(n log n)

Optimal time complexity for comparison-based sorting and the Fast Fourier Transform. Used internally by the HZC compressor’s spectral decomposition.

CS44 — Linear Space

S(n) = O(n)

Linear space complexity bound. Memory scales proportionally with input size.

CS45 — Quantum Query Complexity

Q(n) = O(log n)

Logarithmic quantum query complexity (Grover-type speedup). Theoretical lower bound for quantum search.

CS46 — Amdahl’s Law

P(n) = 1 / [(1 − f) + f/n]

Parallel speedup limit. f is the parallelisable fraction; n is the number of processors. Governs multi-node Zeq computation scaling.

CS47 — Shannon Entropy

E(n) = −∑ p(x) log p(x)

Information entropy — the expected information content of a random variable. Core operator for ZSP key derivation, HZC compression ratio estimation, and XI1 information density calculations.

CS84 — Big-O Definition

f(n) = O(g(n)) ⇔ ∃c, n&sub0; ∀n > n&sub0; : f(n) ≤ c · g(n)

Formal definition of asymptotic upper bound. Used to classify operator computational cost.

CS87 — Kolmogorov Complexity

Ω(x) = min{|p| : U(p) = x}

The shortest program that produces output x on a universal Turing machine U. Theoretical compression limit — used by HZC to benchmark compression ratio against the incompressible floor.

API Usage

Call any operator via the Compute API:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer zk_live_..." \
  -d '{"query": "Shannon entropy of a binary source with p=0.3", "operators": ["CS47, KO42"]}'

The 7-step wizard protocol selects the right operators automatically when you omit the operators field. KO42 is always included.