there is some deep academic research on AI/Machine Learning applied crossword solvers, eg contained in the following paper. the basic effective systems utilize large databases of clue-answer pairs combined with dictionaries. an IR "Information Retrieval" system is built to take a given crossword clue and generate "candidate answers". these are further processed eg with part of speech analyzers to generate different "near" answers and constraint solvers guarantee words fit the current constraints eg other letters already known. the systems somewhat use "trial-and-error" just like humans. it is known/ observed that a lot of crossword puzzles reuse clues in minor variations so these systems have some degree of success just "working from memory" and not necessarily utilizing complex rules.
* Distributional Neural Networks for Automatic Resolution of Crossword Puzzles / Severyn, <PERSON>, <PERSON>, <PERSON>
Automatic resolution of Crossword Puzzles (CPs) heavily depends on the quality of the answer candidate lists produced by a retrieval system for each clue of the puzzle grid. Previous work has shown that such lists can be generated using Information Retrieval (IR) search algorithms applied to the databases containing previously solved CPs and reranked with tree kernels (TKs) applied to a syntactic tree representation of the clues. In this paper, we create a labelled dataset of 2 million clues on which we apply an innovative Distributional Neural Network (DNN) for reranking clue pairs. 716
Our DNN is computationally efficient and can thus take advantage of such large datasets showing a large improvement over the TK approach, when the latter uses small training data. In contrast, when data is scarce, TKs outperform DNNs.
you use the word "understand" in your question. that is a more general question in AI about whether systems that succeed at given AI tasks have demonstrated "understanding". it generally verges on philosophy and there is a sizeable "parallel" philosophical debate about how closely AI is to "real intelligence". much of this started with <PERSON> test in the early 1950s. CS researchers generally take a pragmatic/ empirical, behaviorist stance on this. one can measure human performance on objective tests, and machine performance, and just compare numbers and avoid the far deeper questions (for now) of what constitutes "understanding".
another recent successful system that uses AI but not NNs and is very similar to the crossword "clue/answer" dynamic is Watson built by IBM for the jeopardy game, and decisively beat the best human player(s) at the time. it uses technology called DeepQA which is basically/ roughly an IR and post-processing system, in the vein of expert systems. 64