Constrained Mixed Covering Array

Concept

A Constrained Mixed Covering Array (CMCA) is an extension of a covering array with domain constraints expressed as a Boolean formula in CNF. A CMCA of size N is denoted CMCA(t, k, (v1, …, vk), C), where t is the interaction strength, k is the number of parameters, vj is the number of values for each parameter j, and C is a CNF constraint formula. Every row must satisfy C (domain constraints), and every t-tuple that satisfies C must occur at least once in every N × t sub-array (coverage constraints). Optimal CMCAs are those with the smallest N for which a CMCA exists.

First seen 7/7/2026

Last seen 7/7/2026

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Constrained Mixed Covering Array (CMCA)

Definition

A Constrained Mixed Covering Array (CMCA) is an extension of a Covering Array with constraints. A CMCA of size N is an N × k array A = (a_ij), written as:

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Covering Array extends → 100% 1e

A CMCA is defined as an extension of a Covering Array with constraints.

ASP encoding for strength-2 CMCA finding ← implements 100% 1e

The encoding is specifically for finding strength-2 CMCAs.

ASP encoding for optimal strength-2 CMCA finding ← implements 100% 1e

The encoding finds optimal CMCAs by minimizing the number of rows.

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Covering Array EXTENDS Extracted graph relationship

ASP encoding for strength-2 CMCA finding IMPLEMENTS Extracted graph relationship

ASP encoding for optimal strength-2 CMCA finding IMPLEMENTS Extracted graph relationship

CITATIONS

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[1] A CMCA is an extension of a covering array with constraints, written as CMCA(t, k, (v1, …, vk), C), where C is a Boolean formula in CNF. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[2] A CMCA of size N must satisfy: (1) a_ij ∈ {0, 1, …, v_j − 1}; (2) every row satisfies the constraint C (domain constraints); (3) every N × t sub-array contains all t-tuples satisfying C at least once (coverage constraints). catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[3] A CMCA of size N is optimal if N is the smallest n such that a CMCA of size n exists. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[4] In the standard CMCA definition, the constraint C is a hard constraint; there are no soft constraints. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[5] The phone product line example yields an optimal CMCA(2, 5, 3322, C) of size 9, with 67 total pairs across all interactions of which 57 are valid and 10 are invalid. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[6] The catnap fact format uses p/2 for parameter-value pairs and c/2 for constraint clauses composed of pos/2 and neg/2 literals. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[7] The strength-2 CMCA finding ASP encoding (Listing 2) generates row/column/constraint atoms, enforces exactly one value per parameter via assigned/3, encodes domain constraints, and enforces coverage via covered/4 and pair/4. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[8] The optimal strength-2 CMCA finding ASP encoding (Listing 3) introduces activated/1 atoms, minimizes the number of activated rows, and only generates assignments for activated rows. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming

[9] The catnap basic encoding can be extended with weak coverage constraints (Listing 4) to support CCT under limiting resources, maximizing the number of covered pairs when the initial bound n is below the minimal CMCA size. catnap: Generating Test Suites of Constrained Combinatorial Testing with Answer Set Programming