Project description
Exploiting composition to simplify the complexity of algorithms
As mathematicians began developing computers in the 20th century, going from theory to practice, the field of automata theory was born. Automatons, or automata, are abstract models of simple machines or computing devices that automatically follow a predetermined sequence of operations. Automata help computer scientists to understand how a computer completes functions and solves problems. They also help them understand what it means for a function to be computable or for a question to be "decidable." Composition is an important mechanism in automata theory directly relevant to the decidability problem. The EU-funded FouCo project is investigating composition in automata and how to exploit it for specific applications, reducing the complexity of current algorithms.
Objective
Composition is a key technique in automata theory, used in particular in the model-checking, realisability analysis and automatic synthesis of reactive systems. Typically, when it comes to composition, deterministic automata are used as they behave well when composed with other automata or games. However, determinisation is notoriously complex, both conceptually and computationally. One approach to avoiding determinisation is the notion of Good for Games (GFG) nondeterministic automata, which, despite their nondeterminism, compose well with games. Recent work suggests that the notion of GFG automata, so far only used for composing non-deterministic automata with games, is in fact much more powerful: it generalises to alternating automata, a more general and flexible type of automata that is particularly close to formal logics, and such automata can be used not just in composition with games, but with other automata as well. This means that alternating automata of this type could potentially be used in solutions to parity games, Church's synthesis problem, and, more generally, for turning automata into equivalent automata with simpler acceptance conditions.
This project aims to study how to make automata compositional, how to recognise compositional automata, and how to exploit compositionality to improve algorithms in verification and synthesis. In particular, we will study how partial notions of composition, that is, automata that are not GFG in general, but can still be composed with a restricted class of games, can be exploited to avoid determinisation and thereby simplify existing algorithms for reactive synthesis, model-checking and Markov decision procedures.
Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
L69 7ZX Liverpool
United Kingdom