Linguistic Predictability and Search Complexity: How Linguistic Redundancy Constraints the Landscape of Classical and Quantum Search

TL;DR

This paper explores how linguistic redundancy influences the complexity of classical and quantum search algorithms in decrypting Renaissance Italian texts, revealing a direct relationship between language regularities and search effort.

Contribution

It introduces a hybrid classical-quantum framework that models the impact of linguistic predictability on search complexity using historical Italian texts and quantum-inspired algorithms.

Findings

Search effort scales with 1/sqrt(pgood) as predicted by quantum search theory.

Longer texts produce sharper score distributions and smaller key spaces.

Linguistic redundancy constrains search space, affecting classical and quantum search dynamics.

Abstract

This study examines the quantitative relationship between linguistic regularities and computational search complexity through a hybrid classical-quantum framework applied to Renaissance Italian texts. Using four representative works from the fifteenth and sixteenth centuries-Il Principe (Machiavelli), Il Cortegiano (Castiglione), I Ricordi (Guicciardini), and Orlando Furioso (Ariosto)-we construct character-based n-gram models under both a historically grounded 25-letter orthography and the full modern Italian alphabet. These models provide corpus-derived probabilistic baselines for evaluating substitution-cipher search processes. Combining classical hill climbing and simulated annealing with Grover-style quantum-inspired estimates and a QUBO annealing formulation, we quantify how the probability that a key produces a linguistically plausible decryption (pgood) relates to expected computational effort. Across cipher lengths from 200 to 1000 characters, empirical results confirm the predicted dependence of Grover oracle calls on 1/sqrt(pgood) and show that longer texts yield sharper score distributions and smaller feasible key regions. Overall, the findings establish a link between linguistic redundancy and search-space contraction, providing an empirical framework for comparing classical, quantum-inspired, and idealized quantum search dynamics under unified corpus-driven constraints.