Nir Piterman

Mathieu Lehaut, Nir Piterman

We study an extension of Zielonka's (fixed) asynchronous automata called reconfigurable asynchronous automata where processes can dynamically change who they communicate with. We show that reconfigurable asynchronous automata are not more expressive than fixed asynchronous automata by giving translations from one to the other. However, going from reconfigurable to fixed comes at the cost of disseminating communication (and knowledge) to all processes in the system. We then show that this is unavoidable by describing a language accepted by a reconfigurable automaton such that in every equivalent fixed automaton, every process must either be aware of all communication or be irrelevant.

Daniel Hausmann, Nir Piterman, Irmak Sağlam et al.

We consider two-player games over finite graphs in which both players are restricted by fairness constraints on their moves. Given a two player game graph $G=(V,E)$ and a set of fair moves $E_f\subseteq E$ a player is said to play "fair" in $G$ if they choose an edge $e \in E_f$ infinitely often whenever the source vertex of $e$ is visited infinitely often. Otherwise, they play "unfair". We equip such games with two $ω$-regular winning conditions $α$ and $β$ deciding the winner of mutually fair and mutually unfair plays, respectively. Whenever one player plays fair and the other plays unfair, the fairly playing player wins the game. The resulting games are called "fair $α/β$ games". We formalize fair $α/β$ games and show that they are determined. For fair parity/parity games, i.e., fair $α/β$ games where $α$ and $β$ are given each by a parity condition over $G$, we provide a polynomial reduction to (normal) parity games via a gadget construction inspired by the reduction of stochastic parity games to parity games. We further give a direct symbolic fixpoint algorithm to solve fair parity/parity games. On a conceptual level, we illustrate the translation between the gadget-based reduction and the direct symbolic algorithm which uncovers the underlying similarities of solution algorithms for fair and stochastic parity games, as well as for the recently considered class of fair games where only one player is restricted by fair moves.

Giuseppe De Giacomo, Christian Hagemeier, Daniel Hausmann et al.

We study synthesis for obligation properties expressed in LTLfp, the extension of LTLf to infinite traces. Obligation properties are positive Boolean combinations of safety and guarantee (co-safety) properties and form the second level of the temporal hierarchy of Manna and Pnueli. Although obligation properties are expressed over infinite traces, they retain most of the simplicity of LTLf. In particular, we show that they admit a translation into symbolically represented deterministic weak automata (DWA) obtained directly from the symbolic deterministic finite automata (DFA) for the underlying LTLf properties on trace prefixes. DWA inherit many of the attractive algorithmic features of DFA, including Boolean closure and polynomial-time minimization. Moreover, we show that synthesis for LTLfp obligation properties is theoretically highly efficient - solvable in linear time once the DWA is constructed. We investigate several symbolic algorithms for solving DWA games that arise in the synthesis of obligation properties and evaluate their effectiveness experimentally. Overall, the results indicate that synthesis for LTLfp obligation properties can be performed with virtually the same effectiveness as LTLf synthesis.

Shaun Azzopardi, Luca Di Stefano, Nir Piterman

Recent years have seen a significant increase in the interest in reactive synthesis from specifications that relate to infinite state spaces. We present sweap, a tool for synthesis of infinite-state Linear Integer Arithmetic reactive systems. sweap implements a CEGAR approach, relying on state-of-the-art finite-state synthesis tools as black boxes to solve abstract synthesis problems. sweap supports most common input formalisms for infinite-state reactive-synthesis problems: Temporal Stream Logic Modulo Theories, Reactive Program Games, the bespoke input of the ISSY tool, and our own bespoke input. We present a mature version of sweap with novel features: a dual abstraction approach that improves its capabilities in proving unrealisability, support for nondeterministic and unbounded updates, more general initialization of variables, and equirealisable reductions for optimisation. Experimental evaluation shows that sweap outperforms its only competitor in this domain.

Alexandre Duret-Lutz, Giuseppe De Giacomo, Marcin Jurdzinski et al.

Syntactic obligations are a fragment of LTL formulas that translate to deterministic weak $ω$-automata (DWA). We show that syntactic obligations can be very efficiently converted to minimal DWA represented using multi-terminal binary decision diagrams (MTBDDs), and that synthesis of such specifications can be solved directly on the MTBDD representation on the fly. Our implementation in Spot shows substantial runtime improvements in translation and synthesis.

Daniel Hausmann, Shufang Zhu, Gianmarco Parretti et al. · oxford

Recently, the Manna-Pnueli Hierarchy has been used to define the temporal logics LTLfp and PPLTLp, which allow to use finite-trace LTLf/PPLTL techniques in infinite-trace settings while achieving the expressiveness of full LTL. In this paper, we present the first actual solvers for reactive synthesis in these logics. These are based on games on graphs that leverage DFA-based techniques from LTLf/PPLTL to construct the game arena. We start with a symbolic solver based on Emerson-Lei games, which reduces lower-class properties (guarantee, safety) to higher ones (recurrence, persistence) before solving the game. We then introduce Manna-Pnueli games, which natively embed Manna-Pnueli objectives into the arena. These games are solved by composing solutions to a DAG of simpler Emerson-Lei games, resulting in a provably more efficient approach. We implemented the solvers and practically evaluated their performance on a range of representative formulas. The results show that Manna-Pnueli games often offer significant advantages, though not universally, indicating that combining both approaches could further enhance practical performance.

Yehia Abd Alrahman, Giuseppe Perelli, Nir Piterman

We propose a formalism to model and reason about multi-agent systems. We allow agents to interact and communicate in different modes so that they can pursue joint tasks; agents may dynamically synchronize, exchange data, adapt their behaviour, and reconfigure their communication interfaces. The formalism defines a local behaviour based on shared variables and a global one based on message passing. We extend LTL to be able to reason explicitly about the intentions of the different agents and their interaction protocols. We also study the complexity of satisfiability and model-checking of this extension.