Nomenclature

Abbreviations

Abbreviation	Full form
AI	Artificial Intelligence
APE	Automatic Prompt Engineer
API	Application Programming Interface
APO	Automatic Prompt Optimisation
ASCII	American Standard Code for Information Interchange
ATK	Attack (hero or monster attribute)
BFS	Breadth-First Search
CoT	Chain of Thought
DEF	Defence (hero or monster attribute)
DSPy	Declarative Self-improving Python (prompt-programming framework)
EXP	Experience points
GEPA	Genetic-Pareto prompt optimisation
GRPO	Group Relative Policy Optimization
GWDG	Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen
HP	Hit points
HTML	HyperText Markup Language
JSON	JavaScript Object Notation
LLM	Large Language Model
MDEF	Magic defence (hero attribute subtracted from every fight's damage)
MoE	Mixture of Experts
MT0–MT23	Floors 0 to 23 of the 24-floor tower
OPRO	Optimization by PROmpting
RL	Reinforcement Learning
RLHF	Reinforcement Learning from Human Feedback
RQ	Research Question
SAIA	Scalable AI Accelerator (inference service of the GWDG)
STRIPS	Stanford Research Institute Problem Solver

Symbol	Meaning
$a_h$ , $d_h$	the hero's ATK and DEF
$h_m$ , $a_m$ , $d_m$	a monster's HP, ATK and DEF
$T$	number of hero strikes needed to defeat a monster
$d$	a monster's damage per strike after the hero's DEF (Table 4.1)
$D$	HP cost of a fight
$(S, s_0, A, \delta, G)$	floor task: set of states, initial state, legal actions $A(s)$ , transition, goal (Definition 4.1)
HP $_{\text{final}}$	the hero's HP at the end of an episode
HP $_{\text{opt}}$	exact optimum of a floor: the largest final HP of any winning action sequence
$L$	net lookahead value of an action
$v_i$	HP-equivalent value of an unlocked item $i$
$\lambda_j$	factor for items behind $j$ gateways (1 for $j = 0$ ; 0.7, 0.5 and 0.35 for $j = 1, 2, 3$ )
$c_g$	HP cost of gateway $g$
$C_{\text{route}}$ , $S_{\text{route}}$	HP of fighting needed to reach the stat items behind an action, and the HP these items save on the other listed fights (net stat-route line)

Symbol	Meaning
$N$	number of episodes of a configuration
$k$	commitment: number of actions per model call; in $k/N$ , the number of successful episodes
$\hat p$	success rate $k/N$
$z$	quantile of the standard normal distribution in the Wilson interval ( $z = 1.96$ )
HP/opt	HP $_{\text{final}}$ divided by HP $_{\text{opt}}$ for a successful episode; reported as the mean over successful episodes
$S_{\text{goal}}$	goal score of one episode
$C$	share of a floor's monsters defeated (in $S_{\text{goal}}$ )
$n$ , $b$	in the sign test: number of discordant pairs, and the number of these that favour the first prompt (in Chapter 2, a sequence length and a branching factor)

Symbol	Meaning
$w_t$	the $t$ -th token of a sequence of $n$ tokens
$\Pr(\cdot)$	probability
$Q$ , $K$ , $V$	query, key and value matrices of self-attention
$d_k$	length of the key vectors
$z_i$	score of token $i$ in the model's last layer
$p_i$	probability of token $i$ after the softmax
$\tau$	sampling temperature
$\theta$	parameters of a model
$P$	prompt
$s$ , $a$	state, action
$\pi(a \mid s, P)$	policy: probability of action $a$ in state $s$ under prompt $P$
$G$	number of outputs sampled per input in GRPO (the goal of a floor task in Definition 4.1)
$r_i$	reward of output $i$
$\hat{A}_i$	advantage of output $i$ in GRPO: its reward standardised within its group
$b$	branching factor: number of choices per step of a search
$\ell$	search depth: number of actions from the initial state

Models are named by family, version and total size; the endpoint identifiers are listed in Table 6.1 and Appendix D.

Name	Type and size	Reasoning mode	Used in
Qwen3.5-397B	mixture of experts, 397 B parameters, 17 B active	thinking	main experiments; planning study (Section 6.6); reference and teacher in the first configuration of the first prompt-optimisation study
Qwen3.6-35B	mixture of experts, 35 B parameters, 3 B active	thinking	main experiments; prompt-optimisation study (Section 6.5); exact-route prompt (Section 6.6)
Qwen3.8-27B	dense, 27 B parameters	thinking	planning study (Section 6.6)
DeepSeek-V4-Flash	mixture of experts, 284 B parameters, 13 B active	thinking	main experiments; planning study (Section 6.6); teacher in the second configuration of the first prompt-optimisation study, task model and teacher in Sections 6.5.3 and 6.5.4
DeepSeek-V4-Flash (no thinking)	the same model with its reasoning mode switched off	none	prompt-optimisation study (Section 6.5)
Mistral Medium 3.5	128 B parameters, architecture not stated by the service	none	main experiments
Llama-3.1-8B	dense, 8 B parameters, instruction-tuned	none	prompt-optimisation study (Section 6.5)

B = billion.

Label	Meaning
RQ1–RQ3	research questions (Section 1.1)
HA–HC	hypotheses of the thesis, one per research question (Section 1.1)
R1–R3	rival explanations (Sections 1.1 and 7.2)
S1–S14	strategy principles (Table 4.2)
G1–G5	hypotheses of the prompt-optimisation study, stated before the runs (Section 6.5.1)
P1–P3	predictions for the evolved-route run, stated before the run (Section 6.5.4)
hand01–hand04	hand-designed floors (Table 4.3)
gen01–gen15	generated floors (Table 4.3)
First, second and final tower observation	the three tower observations compared in Table 6.13 (Section 5.5.3); the final one is used for all tower results of Table 6.2

Two labels of the verbatim observation text appear in listings and appendices:

Internal label	Name in this thesis
`effCost`	effective cost
`ORDER` line	fight-order line

The result file behind each reported cell is listed in Table D.4 (Appendix D).