Modern digital technologies—from online platforms and mobile apps to financial trading systems and medical software—rely heavily on reasoning about sequences of data. These sequences may be strings of text, lists of numbers, program arrays, or time-series data. While current computer science methods handle sequences over small, fixed alphabets very well, real-world applications involve infinitely many possible data values, such as numbers, strings, or identifiers.
This mismatch creates major difficulties for verification of software, analysis of data-intensive applications, and explainability of machine learning models. Many critical questions—such as whether a list-manipulating program is error-free, answering a graph database query, or explaining the behavior of a sequential neural model (e.g. a recurrent neural network or a transformer) — remain extremely hard to answer with today’s methods.
The ERC Consolidator Grant LASD (Logic and Automata over Sequences with Data) addresses these challenges by developing new mathematical models (inspired by logic and automata), algorithms, and software tools for reasoning about sequences with complex data. The project focuses on three interconnected scientific hurdles:
- Complex data reasoning: creating expressive yet decidable models that allow arithmetic, string, and other advanced operations.
- Relational reasoning: handling relations between multiple data sequences, e.g. as needed in program analysis.
- Aggregation: supporting operations such as sum, average, or median, which are essential (among others) for database applications.
The expected impact is twofold: advancing fundamental computer science by overcoming long-standing barriers in automata and logic, and developing prototypes showcasing the future potential of a technology transfer in the domains of graph databases, program verification, and interpretable AI.
