engines

Engines — Algorithmic Primitives for Agent Systems

Audience: anyone designing or auditing the moving parts of an agent system. This folder catalogs the small set of well-studied algorithms that, in practice, do the heavy lifting in production agent stacks.

What an "engine" is here

An engine is a named, math-grounded primitive that a workflow leans on. Not a heuristic. Not a vibe-coded scoring function. Each engine ships with:

1. Problem — the question the engine answers.
2. Formula — the math, in one or two equations.
3. Decision rule — the boundary that turns the math into a verdict.
4. Complexity — Big-O for both time and space.
5. Reference implementation pattern — language-neutral pseudocode + dependencies.
6. Failure modes — when this engine breaks or is the wrong tool.

If you can't fill in those six sections, what you have is a heuristic, not an engine.

When to add an engine

Add an engine when the same algorithmic question shows up across two or more of your workflows and either:

• the cost of getting it wrong is high (security scans, trust scoring, destructive ops), or
• the workflow is in a tight loop where a 10× speedup matters (real-time hooks, per-tool-call validation).

Don't add an engine for:

• one-off computations a single workflow does once,
• LLM judgment calls (those belong in a prompt, not a formula),
• anything you'd be embarrassed to publish a derivation for.

Naming and labels

Within a project, engines often carry a project-letter prefix (e.g., H1–H5 for project Hydra, W1–W5 for project Sylph). That's a local convenience. In this catalog, engines are named by what they compute, not where they live:

• agentproof.md — Pre-execution static verification: six structural graph checks + temporal safety policy DFA evaluation (status: concept)
• boundary-segmentation.md — Jaccard-Cosine multi-signal clustering
• calibration.md — Sycophancy-rate calibration via progressive/regressive ratios — turns doubt-engine prose into a measurable axis
• drift-detection.md — Markov drift + EMA learning
• entropy-analysis.md — Shannon entropy
• lcs-alignment.md — Hunt-Szymanski longest common subsequence
• llm-bandit.md — Contextual multi-armed bandit for model-tier routing by cost-adjusted quality reward
• pattern-detection.md — Aho-Corasick multi-pattern matching
• scc.md — Tarjan strongly-connected components
• sprt.md — Wald sequential probability ratio test
• tree-edit.md — Zhang-Shasha tree edit distance
• trust-scoring.md — Beta-Bernoulli conjugate prior

When projects adopt one of these, they typically wrap it with a project-specific signature and label, but the underlying math is the same.

How engines compose with conduct

Engines compute; ../conduct/ modules govern. An engine reports a number; the conduct says what to do with it (escalate, log, abstain, ship). Don't bake decisions into engines — keep the math pure and let the conduct rule on its output.

Example: trust-scoring.md produces a posterior mean ∈ [0, 1]. ../conduct/verification.md decides what threshold gates a destructive op, and ../conduct/failure-modes.md names what kind of failure each band represents.

Reference list

Engine	Algorithm	Best for
Pattern detection	Aho-Corasick	Scan text against a fixed set of patterns in linear time
Entropy analysis	Shannon	Detect high-entropy tokens (secrets, random IDs) without a pattern list
Trust scoring	Beta-Bernoulli	Online posterior estimate of a probability with conjugate updates
Drift detection	Markov + EMA	Catch repeated unproductive patterns in a stream of events
LCS alignment	Hunt-Szymanski	Measure how much of an anchor sequence survives in current state
Tree edit	Zhang-Shasha (or Wagner-Fischer reduction)	Quantify structural change between two trees (ASTs, configs)
Strongly-connected components	Tarjan	Find dependency cycles in O(V+E) over directed graphs
Sequential probability ratio	Wald SPRT	Decide between two hypotheses with the minimum sample count
Boundary segmentation	Jaccard + cosine + time-decay	Cluster a stream of events into discrete tasks
LLM Bandit	Contextual ε-greedy / UCB bandit	Route each invocation to the optimal model tier by cost-adjusted quality reward; warm-starts from a cross-session state file
Agentproof	Six structural graph checks + DFA temporal policy evaluation	Verify an agent workflow statically before execution; returns PASS or FAIL with a witness trace (status: concept)
Calibration	Progressive/regressive sycophancy ratios	Quantify the F01 sycophancy rate over a session and produce a CALIBRATED / SYCOPHANTIC / OVERCORRECTED verdict