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\section{Literature Review: Physics-Driven VM Optimisation}
\label{sec:literature-review}

The central finding of this review is that no prior work combines
real-time metrics-driven optimisation, threshold-based automatic decisions,
and formal-verification compatibility in a single implemented system.

\subsection{VM Optimisation Techniques}

\subsubsection{Offline Profiling and Profile-Guided Optimisation}

Representative works include Calder et al.\ (``Continuous Profiling,''
TOCS 1997), Knowles et al.\ (PASTE 2005), and GCC's \texttt{-fprofile-use}
implementation. These approaches collect data in a separate profiling phase,
analyse it offline, and recompile. They are portable and produce predictable
results, but are reactive: they require re-profiling for different workloads
and cannot adapt at runtime.

StarForth's approach is online and adaptive; no separate profiling phase
is required.

\subsubsection{Adaptive Optimisation and Tiered Compilation}

Representative works include Hölzle, Chambers, and Ungar
(``Inline Caches,'' PLDI~1991), IBM's Jikes RVM adaptive optimisation
system, and Oracle HotSpot's tiered compilation. These systems collect
metrics during execution and dynamically recompile hot paths, achieving
30--100$\times$ speedup on some workloads. However, they require an
embedded compiler, are difficult to verify formally, and are incompatible
with microkernel capability models.

StarForth achieves a measured 1.78$\times$ speedup without code generation,
representing a simpler alternative for systems where dynamic code generation
is prohibited.

\subsubsection{Just-In-Time Compilation}

Representative works include Dynamo (Bala et al., PLDI~2000), HotSpot
(Paleczny et al., JVM Performance Workshop~2001), and V8 (various). JIT
compilation offers maximum performance but carries substantial complexity,
hard formal-verification properties, memory overhead, and is incompatible
with formal methods and microkernel isolation.

\subsection{Real-Time Metrics-Driven Systems}

\subsubsection{Hardware Performance Monitoring}

Intel VTune, AMD CodeXL, and ARM Streamline use CPU performance counters
for real-time feedback. These are accurate and low overhead, but
platform-specific and frequently privileged.

StarForth uses application-level execution frequency counters
(\texttt{execution\_heat}), which are portable, require no privileged access,
and carry clear semantic meaning.

\subsubsection{Application-Level Instrumentation}

Representative works include Valgrind (Nethercote and Seward, PLDI~2007)
and DynamoRIO (Bruening et al., PLDI~2003). These frameworks are flexible
but carry overhead and are designed for offline analysis.

StarForth uses lightweight counters with negligible overhead and makes
online decisions in real time.

\subsection{Physics-Inspired and Biologically-Inspired Computing}

\subsubsection{Swarm and Thermodynamic Models}

Particle swarm optimisation (Kennedy and Eberhart, ICNN~1995), ant colony
optimisation (Dorigo et al., 1996), and thermodynamic scheduling models
(Karlin et al., ICCD~2002) borrow physical metaphors. Most are theoretical,
probabilistic, or limited to specific domains.

StarForth uses the physics analogy as a modelling language while relying on
deterministic threshold logic. \texttt{execution\_heat} is a concrete metric,
not merely an analogy: it is an exact execution frequency counter. The
thermodynamic vocabulary motivates the mathematics without becoming the
claim.

\subsection{Formal Verification of VM Optimisation}

\subsubsection{Verified Compilers and Virtual Machines}

Representative works include CompCert (Leroy et al., POPL~2006) and CakeML
(Kumar et al., ICFP~2014). Machine-checked correctness proofs provide maximum
assurance but require substantial ongoing effort.

StarForth is designed for verification from the outset: pure Q48.16
fixed-point arithmetic throughout, no dynamic code generation, and
deterministic logic. Isabelle/HOL proofs cover all seven feedback loops and
five word categories. The physics-driven optimisations are performance-only
(cache hit $=$ bucket hit $=$ same word found), requiring no semantic-change
proofs.

\subsection{Stack-Based and FORTH Virtual Machines}

FORTH optimisation literature (Ting, Appel, Bell Labs technical reports)
identifies direct threading, inline caching, and stack operation fusion as
the classical techniques. StarForth implements direct threading and treats
the physics-driven approach as orthogonal and additive. This is the first
application of real-time metrics-driven optimisation to a FORTH VM.

\subsection{Microkernel-Compatible Systems}

seL4 (Klein et al., SOSP~2009) and L4 (Liedtke, ASPLOS~1996; Heiser and
Elphinstone, SOSP~2016) require that VM optimisation respect the capability
model. JIT compilation violates this constraint by generating arbitrary code.
StarForth's physics-driven approach is explicitly designed for L4Re
compatibility, enabling formal verification while maintaining microkernel
isolation.

\subsection{The Novelty Gap}

\begin{center}
\begin{tabular}{lcccc}
\toprule
Approach & Performance & Verifiable & L4Re Compatible & Complexity \\
\midrule
Offline profiling  & $1.05\times$ & Yes & Yes & Medium \\
JIT compilation    & $5\text{--}30\times$ & No  & No  & High \\
\textbf{Physics-driven} & \textbf{1.78$\times$} & \textbf{Yes} & \textbf{Yes} & \textbf{Low} \\
\bottomrule
\end{tabular}
\end{center}

StarForth occupies a unique position: the only implemented system combining
real-time metrics collection, automatic threshold-based decisions, and
verifiable arithmetic at VM scale. JIT researchers accept complexity to
maximise performance; verification researchers accept lower performance to
maximise correctness; microkernel researchers prioritise isolation.
StarForth integrates all four concerns.

\subsection{Recommended Citations}

\textbf{Core optimisation:} Hölzle et al.\ (PLDI~1991); Paleczny et al.\
(2001); Lattner and Adve (ASPLOS~2004).

\textbf{Metrics and profiling:} Nethercote and Seward (PLDI~2007); Berger
et al.\ (PLDI~2001).

\textbf{Formal verification:} Leroy et al.\ (POPL~2006); Klein et al.\
(SOSP~2009).

\textbf{Physics-inspired and statistical:} Kennedy and Eberhart (ICNN~1995);
Gelman et al., \textit{Bayesian Data Analysis}, 3rd ed.

\textbf{FORTH and stack machines:} Ierusalimschy et al.\
(JUCS~2006); Appel, \textit{Compiling with Continuations} (1992).

\textbf{Microkernels:} Liedtke (ASPLOS~1996); Heiser and Elphinstone
(SOSP~2016).

\subsection{Positioning Statement}

Virtual machine optimisation has historically pursued two divergent paths:
offline profiling (simple but reactive) and JIT compilation (responsive but
complex and difficult to verify). StarForth presents a third approach:
physics-inspired real-time metrics-driven optimisation. By tracking word
execution frequency (\texttt{execution\_heat}) and promoting
frequently-executed words to an LRU cache via threshold-based logic, the
system achieves a 1.78$\times$ performance improvement without code
generation, offline profiling, or manual tuning. The approach is compatible
with formal verification (pure Q48.16 fixed-point arithmetic) and microkernel
constraints (no dynamic code generation). Bayesian statistical inference
validates the results, and the framework extends to nine additional
optimisation opportunities, suggesting a cumulative improvement of 5--8$\times$.