Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation
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arXiv
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| Natura: | Preprint |
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2025
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| author | Arafat, Jahidul Tasmin, Fariha Poudel, Sanjaya |
| author_facet | Arafat, Jahidul Tasmin, Fariha Poudel, Sanjaya |
| contents | Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment, we present the first comprehensive CSP formulation of Wordle with novel constraint-aware solving strategies. We introduce CSP-Aware Entropy, computing information gain after constraint propagation rather than on raw candidate sets, and a Probabilistic CSP framework integrating Bayesian word-frequency priors with logical constraints. Through evaluation on 2,315 English words, CSP-Aware Entropy achieves 3.54 average guesses with 99.9% success rate, a statistically significant 1.7% improvement over Forward Checking (t=-4.82, p<0.001, Cohen's d=0.07) with 46% faster runtime (12.9ms versus 23.7ms per guess). Under 10% noise, CSP-aware approaches maintain 5.3 percentage point advantages (29.0% versus 23.7%, p=0.041), while Probabilistic CSP achieves 100% success across all noise levels (0-20%) through constraint recovery mechanisms. Cross-lexicon validation on 500 Spanish words demonstrates 88% success with zero language-specific tuning, validating that core CSP principles transfer across languages despite an 11.2 percentage point gap from linguistic differences (p<0.001, Fisher's exact test). Our open-source implementation with 34 unit tests achieving 91% code coverage provides reproducible infrastructure for CSP research. The combination of formal CSP treatment, constraint-aware heuristics, probabilistic-logical integration, robustness analysis, and cross-lexicon validation establishes new performance benchmarks demonstrating that principled constraint satisfaction techniques outperform classical information-theoretic and learning-based approaches for structured puzzle-solving domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation Arafat, Jahidul Tasmin, Fariha Poudel, Sanjaya Computation and Language Artificial Intelligence 68T20, 90C27 I.2.8; I.2.3; G.1.6 Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment, we present the first comprehensive CSP formulation of Wordle with novel constraint-aware solving strategies. We introduce CSP-Aware Entropy, computing information gain after constraint propagation rather than on raw candidate sets, and a Probabilistic CSP framework integrating Bayesian word-frequency priors with logical constraints. Through evaluation on 2,315 English words, CSP-Aware Entropy achieves 3.54 average guesses with 99.9% success rate, a statistically significant 1.7% improvement over Forward Checking (t=-4.82, p<0.001, Cohen's d=0.07) with 46% faster runtime (12.9ms versus 23.7ms per guess). Under 10% noise, CSP-aware approaches maintain 5.3 percentage point advantages (29.0% versus 23.7%, p=0.041), while Probabilistic CSP achieves 100% success across all noise levels (0-20%) through constraint recovery mechanisms. Cross-lexicon validation on 500 Spanish words demonstrates 88% success with zero language-specific tuning, validating that core CSP principles transfer across languages despite an 11.2 percentage point gap from linguistic differences (p<0.001, Fisher's exact test). Our open-source implementation with 34 unit tests achieving 91% code coverage provides reproducible infrastructure for CSP research. The combination of formal CSP treatment, constraint-aware heuristics, probabilistic-logical integration, robustness analysis, and cross-lexicon validation establishes new performance benchmarks demonstrating that principled constraint satisfaction techniques outperform classical information-theoretic and learning-based approaches for structured puzzle-solving domains. |
| title | Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation |
| topic | Computation and Language Artificial Intelligence 68T20, 90C27 I.2.8; I.2.3; G.1.6 |
| url | https://arxiv.org/abs/2510.02855 |