Foundations of Composition

Project Information

FouCo

Grant agreement ID: 892704

DOI

10.3030/892704

Project terminated on 31 December 2020

EC signature date 23 March 2020

Start date 1 April 2020

End date 31 March 2022

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 212 933,76

EU contribution

€ 212 933,76

Coordinated by

THE UNIVERSITY OF LIVERPOOL
United Kingdom

Periodic Reporting for period 1 - FouCo (Foundations of Composition)

Reporting period: 2020-04-01 to 2022-03-31

Summary of the context and overall objectives of the project

Composition is a key technique in automata theory, used in particular in the model-checking, realisability analysis and automatic synthesis of reactive systems.

In plain(ish) English, we develop automata (formal acceptors) that are tailored for these tasks: concise and efficient, doing just what they should, and no more. This pushes the envelope of the doable: more problems are within reach for verifying them, more problems are in reach for learning them with guarantees, etc. This can ultimatively lead to better software, better hardware, and better machine learning techniques in some areas.

Thus, while the nature of the project is foundational and we have mainly produced lemmas and theorems, they are on their slow crawl up the technical readiness level and do have the potential to enfold impact.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

We have studied the succinctness of GFG automata, how to recognise compositional automata, and how to exploit compositionality to improve algorithms in verification and synthesis. We have introduced the notion of GFG pushdown automata and studied their computational and descriptive properties.

We co-proposed a successful grant application for the MoVeMnt project, funded by the Icelandic Research Fund, in collaboration with Antonis Achilleos, Luca Aceto, Anna Ingolfsdottir and Adrian Francalanza.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We have shown that alternating GFG automata are exponentially more succinct than deterministic automata, and have developed a matching upper bound, namely an exponential determinisation procedure for alternating GFG automata. Furthermore, we have developed a polynomial-time decision procedure to recognise whether an alternating automaton is GFG for simple acceptance conditions.

We have extended the notion of GFG automata to pushdown automata on both finite and infinite words and have shown these classes to be both more expressive and more succinct than their deterministic counterparts, while their retain excellent algorithmic properties when it comes to the synthesis problem.

Our work on the foundations of compositional automata has brought this class of automata into the limelight. The pathway to application is likely to be via reactive synthesis tools, where GFG automata can bypass complicated determinisation procedures. We have also identified a potential application for alternating GFG automata in bounded synthesis procedures where the synthesis problem is reduced to a constraint satisfaction problem. Using alternating GFG automata in this setting could reduce the size of the contraint system and therefore allow more complex systems to be synthesised. Formal synthesis procedures have enabled the automatic synthesis of circuits for the AMBA Bus Protocol, a widely used industrial on-chip communication specification; developing more powerful synthesis methods using better adapted automata could have a wide industrial impact down the line, leading to more efficient and reliable systems.

The MoVeMnt project, which builds on the research conducten in this action, will ensure that the foundational principles studied in this project continue to be applied within the realm of runtime monitoring over the next three years.