SymbolicLongMemorySequences.jl

Self-Similar Symbols Sequence Synthesis

Long-memory is a feature of many natural sequences, closely relate to statistical self-similarity. In the past, numerical sequences starting with the size of Nile river floods have been the main topic of study. But there are many domains where there are (hypothesised) long-memory sequences that are non-numerical, symbolic sequences. For instance: human writing, DNA, and so forth.

SymbolicLongMemorySequences.jl is a Julia package for generating Long-Range Dependent (LRD) sequences of non-numerical (categorical/symbolic) data. It provides controllable synthetic sequences for testing LRD estimators, probing information-theoretic quantities, and training or stress-testing sequence models on non-language data with language-like long context.

The package was previously developed as S5.jl. It has been renamed to SymbolicLongMemorySequences.jl for Julia package registration, where clear descriptive names are preferred over short acronym-heavy names.

This is an early version. Lots of changes and tests still to come.

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Motivations

SymbolicLongMemorySequences.jl is useful beyond basic generator benchmarking:

• Estimator testing: generate labelled NN-LRD (NonNumerical LRD) sequences where alphabet, marginal distribution, local structure, and nominal LRD mechanism are known.

• Information-theoretic experiments: create controlled cases for ideas such as excess entropy rate, entropy-rate convergence, and the gap between local and long-range predictability in LRD processes.

• Non-language sequence modelling: train or stress-test LLM-style neural sequence models on symbolic data that is not text, such as event logs, vulnerability classes, genomic symbols, workflow traces, or synthetic protocol states.

• Context-length diagnostics: test whether models exploit genuinely long context rather than only short-range bigram/trigram cues.

• Anomaly and change-detection studies: create controlled shifts in marginal, local Markov structure, regime persistence, or long-range behaviour.

• Privacy-preserving simulation: produce synthetic categorical sequences with realistic burstiness without copying a sensitive corpus.

These applications require the abililty to generate

• very long sequences (million or billions of tokens seems a reasonable starting point); with

• control over short-term behaviour (marginals) as well as enforcing long-memory.

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Background

Long-Range Dependence (LRD) means that the large-scale statistical structure of a sequence is as important as its short-range structure. Formally, a sequence is LRD if its autocovariance function (ACF) decays as a power law,

$$\gamma_k \sim c_\gamma |k|^{-\beta}, \quad \beta \in (0, 1),$$

so that the sum of the tail ACF diverges. LRD is characterised by closely related parameters: the ACF decay exponent $\beta$, the spectral exponent $\alpha = 1 - \beta$, and the Hurst parameter $H = (2 - \beta)/2$ with $H \in (1/2, 1)$.

LRD is ubiquitous in human-generated data (text, Internet traffic, genomics, social media), yet almost all synthesis tools target numerical data. SymbolicLongMemorySequences.jl fills that gap for symbol sequences — data that takes values in a finite, unordered alphabet such as {Orange, Apple, Pear, ...} or {G, A, C, T}.

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Implemented Methods

Methods are broadly classified into property-based and model-based. The former largely aim to synthesize LRD by starting with a numerical sequence with known LRD properties and then crafting a symbolic sequence by transforming the numerical data. The latter start from a model that has properties such as hierarchical structure or power-law distributed times to drive the sequence generation directly.

The model taxonomy is summarized below. MB1 and MB4 are shown as subfamilies because their variants make materially different tradeoffs.

Complexity notation used below:

• n: generated sequence length;
• d: configured history depth or effective memory cutoff;
• k: alphabet size;
• I: number of calibration iterations.

Standard cases can be constructed through the uniform factory API:

using SymbolicLongMemorySequences, StableRNGs

alphabet = [:a, :b, :c]
g = make_generator(:PB1, alphabet; H = 0.8, marginal = [0.2, 0.3, 0.5])
seq = generate(g, 10_000; rng = StableRNG(42))

method_ids()
method_info(:PB1).defaults
method_parameters(:PB1)

make_generator(id, alphabet; kwargs...) accepts IDs such as :PB1, "MB1c", or type-name aliases such as :SpectralFGN. It is intended for common starting points. Use method_parameters(id) to inspect accepted keyword names, defaults, domains, and short descriptions. The explicit constructors below remain the full-control API.

Property-Based Methods

These generate one or more underlying numerical LRD processes and then map them to symbols. In code, this can now be expressed directly as a composition of a LatentSource and a Symbolizer:

source = SpectralFGNSource(0.8)
symbolizer = QuantileSymbolizer([:a, :b, :c], [0.2, 0.3, 0.5])
g = PropertyBasedGenerator(source, symbolizer)
seq = generate(g, 10_000; rng = StableRNG(42))

The named PB methods remain the standard, documented cases. The composable API makes the latent-source/symbolization split explicit, while still checking compatibility at construction time. For example, a quantile symbolizer needs one latent series, an argmax symbolizer needs one latent series per symbol, and an intermittent-map source is currently single-stream only.

For validation and research workflows, property-based generators also expose the numerical process before symbolization:

seq, latent = generate_with_latent(g, 10_000; rng = StableRNG(42))
size(latent)  # width × n

This is useful when a symbolic diagnostic looks weak: the latent ACF and spectrum can be checked separately from the quantization, argmax, or Markov-regime transformation.

Named method	Latent source	Symbolizer
PB1	SpectralFGNSource	QuantileSymbolizer
PB2	SpectralFGNSource	ArgmaxSymbolizer
PB3	SpectralFGNSource or HaarLRDSource	MarkovRegimeSymbolizer
PB4	IntermittentMapSource	QuantileSymbolizer

The LRD property is inherited from the numerical layer, then altered by the symbolization step. Validation therefore reports the behavior of the full composition, not just the latent process.

ID	Name	LRD mechanism	Short-range control	Complexity	Novel?
PB1	Spectral fGn + quantization	Spectral $1/f^\alpha$ shaping	Poor (set by quantization)	$O(n \log n)$	No
PB2	Latent Gaussian categorical (LGCM)	fGn streams + argmax	Via calibrated offsets	$O(n k I)$	No
PB3	Spectral/wavelet driver + Markov state machine	Latent LRD driver rank-binned into regimes	Markov transition matrices	$O(n \log n + n k)$	Partial
PB4	Intermittent map + quantization	Latent intermittent dynamics	Poor (set by quantization)	$O(n \log n)$	No

PB1 — Spectral fGn + quantization. Fractional Gaussian noise with Hurst parameter $H$ is synthesized using the fast, approximate spectral method of Paxson (1997). The real-valued output is sorted into $k$ rank bins; each bin maps to one symbol, with integer bin counts chosen to match a target marginal distribution as closely as possible for the finite sample. This is the simplest approach and serves as the primary validation baseline.

PB2 — Latent Gaussian categorical model (LGCM). A vector of $k$ latent fGn streams is generated, one stream per symbol. At each time step the symbol is the argmax of the latent vector plus calibrated per-symbol offsets. The offsets shift marginal probabilities while the latent streams carry the LRD structure. This is a practical finite-sample approximation to the latent Gaussian categorical model of Gal, Chen & Ghahramani (ICML 2015).

PB3 — Latent LRD driver with a Markov state machine. A latent long-memory driver controls which Markov regime is active at each step. Each regime has its own symbol transition matrix, so local bigram structure can be prescribed while the latent driver injects persistence across scales. The default driver = :spectral uses approximate spectral fGn synthesis followed by rank-binning into regimes; driver = :haar retains the original Haar-like cascade as a comparison path. This is a practical implementation of the wavelet/state-machine idea in Roughan, Veitch & Abry (2000), with a fully calibrated wavelet variant left as a research extension.

PB4 — Intermittent map + quantization. A Pomeau-Manneville-style intermittent map generates a latent real-valued driver with long laminar episodes. The driver is rank-binned to symbols, so finite-sample marginal counts are controlled in the same spirit as PB1. This keeps the method in the property-based family: long-range structure lives in a latent dynamical system, not in an explicit symbolic transition rule.

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Model-Based Methods

These produce LRD through the stochastic model itself rather than via mapping.

ID	Name	LRD mechanism	Short-range control	Complexity	Novel?
MB1a	Linear-Additive Markov Process (LAMP)	Exact power-law history weights	History-weighted transition matrix	$O(n \cdot \min(d,n))$	No
MB1b	Dyadic-bucket LAMP	Dyadic approximation to power-law history	History-weighted transition matrix	$O(n k \log n \log \min(d,n))$	Partial
MB1c	Calibrated additive Markov chain	Centered power-law memory function	Symbol recurrence through additive memory	$O(n \cdot \min(d,n))$	No
MB2	Heavy-tailed On/Off doubly-stochastic Markov chain	Pareto regime sojourn times	Per-regime Markov chains	$O(n \cdot k)$	No
MB3	Fractal Symbol Sequence (FSS) via FRP/FSNP	Fractal point process inter-arrivals	Poor (independent streams)	$O(n \cdot k)$	Yes
MB4a	Normalized Hawkes-style symbolic process	Normalized power-law self/cross-excitation	Excitation matrix	$O(n \cdot k \cdot \min(d,n))$	No
MB4b	Self-exciting mass process	Unnormalized power-law self/cross-excitation mass	Target marginal plus excitation matrix	$O(n \cdot k \cdot \min(d,n))$	Partial
MB4c	Logit self-exciting mass process	Centered log-contrast of unnormalized power-law mass	Target marginal plus excitation matrix	$O(n \cdot k \cdot \min(d,n))$, or $O(n^2 k)$ for full history	Yes
MB5	Duplication-mutation growth	Power-law lag copy/mutate growth	Poor (copy structure induced by growth)	$O(n \log d + d)$	No

MB1a/MB1b/MB1c — Additive history models. Transition probabilities are a weighted sum over transition-matrix rows selected by the observed history,

$$q(s) = (1-\epsilon)\sum_{k=1}^{d} w_k \cdot P[X_{t-k}, s] + \epsilon p(s),$$

with weights $w_k \propto k^{-(1+\beta)}$ targeting a power-law decay up to the finite observed history range. If d exceeds the sequence length, only observed history contributes and the missing pre-history mass is assigned to the target marginal. The default transition matrix is identity, recovering copy-from-history behavior. A simple repeat-biased choice is lamp_repeat_transition(marginal; repeat_probability), an identity/dyad mixture whose dyad rows equal the requested marginal. The small innovation term $\epsilon p(s)$ keeps the requested marginal distribution active after initialization and prevents finite-history absorption. The Custom Decay Language Model (CDLM) of Singh, Greenberg & Klakow (2016) is a close variant demonstrated on text. For large alphabets the weight tensor may be compressed via low-rank approximations.

LAMP is now treated as MB1a, the exact finite-history implementation. It is useful for testing and moderate sequence lengths, but becomes expensive when d >= n. DyadicLAMP is MB1b, a scalable approximation that groups history lags into dyadic age buckets such as 1, 2:3, 4:7, and so on. Each bucket contributes its total power-law weight times the empirical symbol mix in that age range. MB1b keeps the same transition-matrix controls while making much larger effective memory depths feasible.

CalibratedAdditiveMarkov is MB1c, a centered additive Markov-chain memory function:

$$q(s) = p(s) + \rho \sum_{k=1}^{d} w_k \left(1[X_{t-k}=s] - p(s)\right),$$

with $w_k \propto k^{-\beta}$ and $\rho \in [0,1]$. It is closer to the additive Markov-chain memory-function literature than LAMP's transition-row mixture, and is the clearest path toward future correlation-calibrated symbolic generators.

MB2 — Heavy-tailed On/Off doubly-stochastic Markov chain. The sequence is generated by a Markov chain that alternates between two or more regimes. Sojourn times in each regime follow a Pareto distribution with tail index $\alpha \in (1, 2)$, so the variance of the symbol count function grows super-linearly, with nominal $H = (3 - \alpha)/2$. Within each regime a standard (SRD) Markov chain governs symbol emissions, giving direct control of local statistics. Analogous to Fractal Shot Noise Processes adapted to symbol sequences (Ryu & Lowen 1998; Garrett & Willinger 1994).

MB3 — Fractal Symbol Sequence (FSS) via FRP/FSNP. Each symbol $s_i$ is assigned an independent Fractal Renewal Process (FRP) or Fractal Shot Noise Process (FSNP) governing the times at which that symbol is emitted. The final sequence merges all symbol streams, with the earliest pending event at each step determining the output. LRD arises in each symbol's count process through heavy-tailed inter-arrival times. The known "missing scales" pitfall of naive FRP construction (Roughan, Yates & Veitch 1999) is addressed by using FSNP or a corrected FRP with a verified scale range.

MB4a/MB4b/MB4c — Hawkes-style self-exciting symbol processes. HawkesSymbol is retained as MB4a, a normalized discrete-time analogue of Hawkes-process word-occurrence models. Each symbol has a positive baseline intensity, and each recent symbol adds a power-law weighted row of an excitation matrix to the current intensity vector. This follows the self-excitation idea in Hawkes processes and is motivated by Ogura, Hanada, Amano & Kondo (2022), who model long-range dynamic correlations of word occurrences in written text with Hawkes processes. However, MB4a normalizes the memory kernel before the categorical draw. In validation this can produce local burstiness while leaving a nearly white centered one-hot spectrum, so MB4a is best treated as a cautionary baseline.

SelfExcitingMass is MB4b, the recommended replacement. It uses a default symbol mass in the direction of the requested marginal plus an unnormalized power-law self-excitation mass. The categorical probabilities are normalized only after these masses are added. The default mass and smoothing floor keep all symbols reachable and stabilize startup; the unnormalized history mass lets self-excitation dominate over long represented scales when the data support it. This is a discrete-time categorical adaptation of Hawkes-style self-excitation, not a fitted continuous-time Hawkes process.

LogitSelfExcitingMass is MB4c, an experimental contrast version motivated by the remaining flat-spectrum behavior of MB4b. It first builds the same kind of unnormalized power-law mass, then converts the mass vector to centered log-mass contrasts and samples with weights proportional to marginal[j] * exp(contrast_strength * contrast[j]). This removes common-mode growth in the total history mass before the final categorical normalization. Validation smoke tests show that larger contrast_strength can steepen the spectrum, but too much contrast causes symbol lock-in and poor marginal control, so MB4c should currently be treated as a tunable experimental model rather than as a solved replacement.

For MB4b and MB4c, beta is the asymptotic power-law decay exponent. The offset c is only a short-lag regularizer: using c = 0 gives the clean discrete-time kernel lag^(-beta), while positive c softens the first few lags and delays the apparent power-law onset. The depth d should be read as a computational truncation of an intended long or infinite memory kernel. In MB4c, d = nothing uses all previous generated observations, which is conceptually clean but costs $O(n^2 k)$ in the direct implementation.

MB5 — Duplication-mutation symbolic growth. DuplicationMutation starts from an iid seed and grows the sequence by repeatedly copying from a power-law-distributed previous lag and mutating copied symbols. The method is motivated by expansion-modification and duplication-mutation models for DNA-like symbolic sequences; it is a finite copy/mutate simulator, not a biological genome model. The lag-copy mechanism is deliberate: validation showed that power-law block lengths with uniformly chosen source blocks mostly created local patches rather than the intended decaying autocorrelation curve.

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Controllability

All implemented generators accept an explicit ordered alphabet and reject duplicate alphabet entries. target_marginal(g) reports the marginal distribution the generator claims to target; empirical_marginal(seq, alphabet) and empirical_bigram(seq, alphabet) provide lightweight checks for simulated data.

Type	Alphabet	Marginal control	Bigram/trigram control
SpectralFGN	explicit alphabet	direct marginal; rank binning gives near-exact finite-sample counts	no direct control
LGCM	explicit alphabet	direct marginal; calibrated latent offsets	no direct control
WaveletMarkov	explicit alphabet	aggregate stationary marginal implied by regimes	direct per-regime bigram matrices
IntermittentMapSymbols	explicit alphabet	direct marginal; rank binning gives near-exact finite-sample counts	no direct control
LAMP	explicit alphabet	direct marginal mixed through epsilon; larger epsilon improves marginal control but weakens history dependence	exact history-weighted transition matrix
DyadicLAMP	explicit alphabet	direct marginal mixed through epsilon; larger epsilon improves marginal control but weakens history dependence	dyadic-bucket approximation to history-weighted transition matrix
CalibratedAdditiveMarkov	explicit alphabet	centered additive memory around marginal; strength = 0 is iid	additive memory induces recurrence, not arbitrary bigrams
OnOffMarkov	explicit alphabet	aggregate stationary marginal implied by regimes	direct per-regime bigram matrices
FSS	explicit alphabet	rates / sum(rates) asymptotically	no direct control
HawkesSymbol	explicit alphabet	baseline distribution reported, but output marginal is implied by excitation and finite history	normalized excitation matrix induces bursty local structure; retained as MB4a
SelfExcitingMass	explicit alphabet	default marginal target, but strong excitation can distort finite-sample marginals	unnormalized excitation mass induces long-context recurrence; MB4b recommended
LogitSelfExcitingMass	explicit alphabet	default marginal target, but contrast strength can distort finite-sample marginals	centered log excitation contrasts induce long-context recurrence; MB4c experimental
DuplicationMutation	explicit alphabet	seed/mutation replacement distribution; output marginal is shaped by copied history	copy/mutate growth induces local and long-context structure

For regime-driven methods (WaveletMarkov and OnOffMarkov), symbol-level ACF and spectrum diagnostics only see the LRD regime process when regimes have different observable stationary symbol distributions. Regimes with identical stationary marginals can carry latent long memory while looking nearly short-memory to one-hot symbol diagnostics.

Reproducible simulation studies live in validation/. For example:

julia --project=. validation/marginal_control.jl
julia --project=. validation/local_structure.jl
julia --project=. validation/lrd_method_diagnostics.jl
julia --project=validation validation/longmemory_comparison.jl

These studies test controllability of simulated data; LRD-parameter estimation is intended for a future separate estimator package.

The marginal-control validation includes a paper-ready uniform categorical test with k = 8. For each method it drops the first and last 10% of the generated sequence, compares the remaining symbol frequencies with the intended uniform marginal, writes a CSV table of chi-squared diagnostics, and creates a combined histogram grid under validation/results/marginal_control/. The chi-squared p-values use the iid multinomial reference distribution, so they are useful frequency diagnostics rather than exact hypothesis tests for dependent LRD sequences. In fact, LRD can make empirical marginals converge more slowly than the iid multinomial model assumes, so the strict chi-squared reference is often too conservative even though large values remain indicative of a control issue. The same CSV also reports an approximate effective-sample-size correction: centered one-hot indicators are used to estimate an integrated autocorrelation time for each symbol, the smallest symbol ESS is used as a conservative sequence-level effective_n, and the chi-squared statistic is scaled by effective_n / trimmed_n. These ESS-adjusted p-values are still diagnostics, not exact dependent categorical tests, but they are less misleading for strongly dependent sequences than the iid reference alone. The CSV reports both full-sequence and trimmed-window marginal errors, because rank-binning or empirical calibration can control the whole generated sample while an interior window still fluctuates under dependence. For the LAMP-family marginal-control cases, validation uses lamp_repeat_transition(p; repeat_probability = 0.4), whose stationary distribution is the requested marginal. The pure identity transition remains available as a stress case but can preserve early imbalances for a long time.

The LRD diagnostic transformation is formalized in validation/lrd_symbol_diagnostics.jl: symbols are converted to centered one-hot numeric series before autocorrelation, autocovariance, and periodogram calculations. The LongMemory.jl comparison script documents and tests the needed adaptations to LongMemory.jl's lag and frequency conventions. Autocorrelation validation plots include dashed vertical interpretation limits: a finite-sample n / 10 lag limit, and explicit generator limits where they exist, such as LAMP.d. Spectrum plots show the same scales as reciprocal frequencies. Where the model has a defensible asymptotic-onset scale, plots also mark an approximate power-law onset. For example, OnOffMarkov uses its Pareto scale L_min, while HawkesSymbol, SelfExcitingMass, and LogitSelfExcitingMass use the lag where the offset kernel (lag + c)^(-beta) reaches 90% of its asymptotic log-log slope. Autocorrelation plots also include a gray dashed nominal power-law reference line with slope lag^(-beta), anchored to the first positive plotted autocorrelation value. Power-spectrum plots include the corresponding gray dashed low-frequency reference with slope frequency^(beta - 1).

Current MB4a (HawkesSymbol) diagnostics should be read cautiously: the finite discrete-time normalized implementation can produce short-range burstiness while its centered one-hot power spectrum remains close to white noise. MB4b (SelfExcitingMass) addresses the main failure mode by leaving the power-law memory mass unnormalized until the final categorical draw, while retaining a small default/smoothing mass for support and stability. MB4c (LogitSelfExcitingMass) applies centered log contrasts to reduce common-mode normalization, but can lock onto too few symbols when the contrast is too strong. Both MB4b and MB4c should still be validated empirically rather than treated as theorem-backed LRD constructions.

Validation policy is documented in VALIDATION_POLICY.md. The fast package test suite remains the main development pathway, while larger empirical studies are run manually or behind explicit flags such as SLMS_VALIDATION_LARGE=true.

Benchmarks live in benchmark/ and use a separate Project.toml with BenchmarkTools.jl:

julia --project=benchmark benchmark/benchmarks.jl
SLMS_BENCHMARK_LARGE=true julia --project=benchmark benchmark/benchmarks.jl
SLMS_BENCHMARK_SCALING=true julia --project=benchmark benchmark/benchmarks.jl

The default benchmark run writes benchmark/RESULTS.md, a CSV table under benchmark/results/benchmarks.csv, histogram-style relative-time SVGs, and log-log scaling plots by alphabet size. The retained scaling results use n = 100, 1_000, 10_000, 100_000, 1_000_000, defer k = 64, and average each BenchmarkTools trial over 10 independently seeded syntheses. They show the expected cost split: direct sequential methods such as OnOffMarkov, FSS, and DuplicationMutation are fastest, FFT/rank-binning methods scale well with n, LGCM grows with alphabet size, and explicit history methods such as LAMP, HawkesSymbol, SelfExcitingMass, LogitSelfExcitingMass, and DyadicLAMP pay for their configured memory depth.

First-order local-structure controls use MarkovSpec. Trigram diagnostics are available through empirical_trigram, but a concrete trigram-control specification is intentionally left for future work. The code now exposes LocalStructureSpec and local_structure_order as the extension path for that higher-order API. For one-step Markov behavior, direct matrix testing has k^2 cells and quickly needs much more data than marginal testing. A practical shortcut is to test low-dimensional contrasts of the transition matrix: repeat probability, selected row total-variation errors, stationary-weighted row error, and application-level symbol groups, while reserving full row-by-row tests for smaller alphabets or large validation runs.

A more formal marginal test than the approximate ESS-adjusted chi-squared diagnostic would estimate the null distribution under dependence. Practical options are block/subsampling tests or a parametric Monte Carlo envelope generated from the same configured method. Those are validation extensions rather than fast package tests.

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References

• Paxson, V. (1997). Fast, approximate synthesis of fractional Gaussian noise. CCR 27.
• Dieker, T. (2004). Simulation of fractional Brownian motion. PhD thesis, U. Twente.
• Roughan, M., Veitch, D., & Abry, P. (2000). Real-time estimation of LRD parameters. IEEE/ACM ToN 8(4).
• Gal, Y., Chen, Y., & Ghahramani, Z. (2015). Latent Gaussian processes for distribution estimation of multivariate categorical data. ICML.
• Li, W. (1991). Expansion-modification systems: a model for spatial 1/f spectra. Physical Review A 43.
• Li, W., Marr, T. G., & Kaneko, K. (1994). Understanding long-range correlations in DNA sequences. Physica D 75.
• Melnyk, S. S., Usatenko, O. V., & Yampol'skii, V. A. (2006). Memory functions of the additive Markov chains. Physica A 361.
• Mayzelis, Z. A., Apostolov, S. S., Melnyk, S. S., Usatenko, O. V., & Yampol'skii, V. A. (2006). Additive N-step Markov chains as prototype model of symbolic stochastic dynamical systems with long-range correlations.
• Kumar, R., Raghu, M., Sarlós, T., & Tomkins, A. (2017). Linear additive Markov processes. WWW '17.
• Singh, M., Greenberg, C., & Klakow, D. (2016). The custom decay language model. TSD.
• Ryu, B., & Lowen, S. (1998). Point process models for self-similar network traffic. Stochastic Models 14(3).
• Roughan, M., Yates, J., & Veitch, D. (1999). The mystery of the missing scales. Heavy Tails Workshop.
• Provata, A., & Beck, C. (2012). Coupled intermittent maps modelling the statistics of genomic sequences: a network approach. arXiv:1205.2249.
• Pipiras, V., & Taqqu, M. S. (2017). Long-Range Dependence and Self-Similarity. Cambridge UP.

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AI Disclosure

This package was developed with assistance from Claude Sonnet 4.6 (Anthropic), and Codex; AI coding assistants. The design goals, overall architecture, methods design were human, but Claude and Codex contributed to the design of the package architecture, the coding itself, and some of the write-up of synthesis methods.