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MultiwaySystem RF Compatibility

Overview

The MultiwaySystem object provides compatibility with the Wolfram Language ResourceFunction["MultiwaySystem"] (RF). This document covers the standalone API, RF-compatible properties, and behavioral differences.

Standalone API

The 4-argument pattern matches the RF interface:

(* 4-arg: property query *)
MultiwaySystem[rules, init, n, "Property"]

(* 3-arg: defaults to AllStatesList *)
MultiwaySystem[rules, init, n]

Both forms automatically enable "DeduplicateSlices" -> True to match RF behavior.

RF-Compatible Properties

Property Description
"AllStatesList" Sorted, deduplicated states per step
"StatesCountsList" Count of unique states per step
"CausalInvariantQ" Confluence check via branch pair resolution
"BranchPairsList" Sorted, deduplicated branch pairs
"CanonicalBranchPairsList" Branch pairs from LHS overlaps (distinct rules required)
"AllEventsList" Events with {rule, LHS, {prefix, suffix}} format
"StatesGraph" States evolution graph
"BranchialGraph" Branchial connection graph

DeduplicateSlices

The RF's "AllStatesList" deduplicates successor states within each evolution step. Our implementation does this via the "DeduplicateSlices" option:

  • Standalone API (3/4-arg): Enabled automatically
  • Object API (ms["Property", n]): Requires MultiwaySystem[rules, init, "DeduplicateSlices" -> True]
  • Raw Multi: Requires Multi[expr, rules, "DeduplicateSlices" -> True]

CausalInvariantQ Semantics

Checks if the system is confluent — whether all branch pairs resolve (converge) within the evolution steps:

  1. Compute BranchPairResolutionsList up to step n
  2. Find pairs unresolved at step Ceiling[n/2]
  3. Check if ALL such pairs are resolved by step n
  4. If no unresolved pairs exist → True

CanonicalBranchPairsList

Generates branch pairs from LHS overlaps:

  1. Compute suffix-prefix overlaps between all LHS strings
  2. Include each LHS itself (may have multiple applicable rules)
  3. Filter: Keep only strings where ≥2 different rules can apply
  4. For each overlap string, apply all applicable rules to get branch pairs

Important: Same-rule position-branching (e.g., "AA" -> "AB" applied at positions 1 and 2 of "AAA") does NOT count as a canonical branch pair. At least two distinct rules must apply.

AllEventsList Format

Each event is a 3-element list: {rule, LHS, {prefix, suffix}}

  • rule: The applied rule (e.g., "A" -> "ABA")
  • LHS: The left-hand side that was matched (e.g., "A")
  • {prefix, suffix}: The context around the match in the parent state

Testing

# Run RF comparison tests
wolframscript -c 'TestReport["Tests/MultiwaySystemRF-Comparison.wlt"]'