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LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial…

Logic in Computer Science · Computer Science 2016-11-18 Jorge A. Baier , Alberto Camacho , Christian Muise , Sheila A. McIlraith

We study the problem of realizing strategies for an LTLf goal specification while ensuring that at least an LTLf backup specification is satisfied in case of unreliability of certain input variables. We formally define the problem and…

Artificial Intelligence · Computer Science 2024-12-20 Christian Hagemeier , Giuseppe de Giacomo , Moshe Y. Vardi

The classical LTL synthesis problem is purely qualitative: the given LTL specification is realized or not by a reactive system. LTL is not expressive enough to formalize the correctness of reactive systems with respect to some quantitative…

Logic in Computer Science · Computer Science 2013-01-10 Aaron Bohy , Véronique Bruyère , Emmanuel Filiot , Jean-François Raskin

Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a…

Logic in Computer Science · Computer Science 2020-09-24 Andrew M. Wells , Morteza Lahijanian , Lydia E. Kavraki , Moshe Y. Vardi

LTLf synthesis under partial observability requires reasoning about unobservable environment variables, which is typically handled by constructing a belief-state DFA via subset construction that universally quantifies these variables.…

Logic in Computer Science · Computer Science 2026-05-05 Nadav Alon , Supratik Chakraborty , Alexandre Duret-Lutz , Dror Fried , Lucas M. Tabajara , Moshe Y. Vardi , Shufang Zhu

A challenging problem for autonomous systems is to synthesize a reactive controller that conforms to a set of given correctness properties. Linear temporal logic (LTL) provides a formal language to specify the desired behavioral properties…

Formal Languages and Automata Theory · Computer Science 2019-10-08 Rayna Dimitrova , Mahsa Ghasemi , Ufuk Topcu

Reactive synthesis addresses the problem of generating a controller for a temporal specification in an adversarial environment; it was typically studied for LTL. Driven by applications ranging from AI to business process management, LTL…

Logic in Computer Science · Computer Science 2025-08-26 Sarah Winkler

The problem of LTLf reactive synthesis is to build a transducer, whose output is based on a history of inputs, such that, for every infinite sequence of inputs, the conjoint evolution of the inputs and outputs has a prefix that satisfies a…

Formal Languages and Automata Theory · Computer Science 2025-07-04 Alexandre Duret-Lutz , Shufang Zhu , Nir Piterman , Giuseppe de Giacomo , Moshe Y Vardi

Temporal synthesis is the automated design of a system that interacts with an environment, using the declarative specification of the system's behavior. A popular language for providing such a specification is Linear Temporal Logic, or LTL.…

Logic in Computer Science · Computer Science 2020-08-18 Shufang Zhu , Lucas M. Tabajara , Jianwen Li , Geguang Pu , Moshe Y. Vardi

Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to…

Artificial Intelligence · Computer Science 2026-05-28 Yujian Cao , Sven Schewe , Qiyi Tang , Shufang Zhu

Reactive synthesis builds a system from a specification given as a temporal logic formula. Traditionally, reactive synthesis is defined for systems with Boolean input and output variables. Recently, new theories and techniques have been…

Logic in Computer Science · Computer Science 2021-08-03 Benedikt Maderbacher , Roderick Bloem

Given a specification of linear-time temporal logic interpreted over finite traces (LTLf), the reactive synthesis problem asks to find a finitely-representable, terminating controller that reacts to the uncontrollable actions of an…

Formal Languages and Automata Theory · Computer Science 2022-12-22 Luca Geatti , Marco Montali , Andrey Rivkin

In synthesis, assumptions are constraints on the environment that rule out certain environment behaviors. A key observation here is that even if we consider systems with LTLf goals on finite traces, environment assumptions need to be…

Artificial Intelligence · Computer Science 2019-12-18 Shufang Zhu , Giuseppe De Giacomo , Geguang Pu , Moshe Vardi

Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning, control of autonomous systems, and load distribution in power networks. A common specification pattern in such applications…

Logic in Computer Science · Computer Science 2018-04-03 Rayna Dimitrova , Mahsa Ghasemi , Ufuk Topcu

In this paper, we study incremental LTLf synthesis -- a form of reactive synthesis where the goals are given incrementally while in execution. In other words, the protagonist agent is already executing a strategy for a certain goal when it…

Artificial Intelligence · Computer Science 2026-03-03 Giuseppe De Giacomo , Yves Lespérance , Gianmarco Parretti , Fabio Patrizi , Moshe Y. Vardi

We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLT) from LTL formulae via reachability…

Systems and Control · Electrical Eng. & Systems 2020-07-07 Yulong Gao , Alessandro Abate , Frank J. Jiang , Mirco Giacobbe , Lihua Xie , Karl H. Johansson

Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL).…

Logic in Computer Science · Computer Science 2018-03-28 Bernd Finkbeiner , Felix Klein

We discuss the problem of experimentally evaluating linear-time temporal logic (LTL) synthesis tools for reactive systems. We first survey previous such work for the currently publicly available synthesis tools, and then draw conclusions by…

Logic in Computer Science · Computer Science 2011-02-22 Rüdiger Ehlers

We reduce synthesis for CTL* properties to synthesis for LTL. In the context of model checking this is impossible - CTL* is more expressive than LTL. Yet, in synthesis we have knowledge of the system structure and we can add new outputs.…

Formal Languages and Automata Theory · Computer Science 2017-11-30 Roderick Bloem , Sven Schewe , Ayrat Khalimov

We present the Temporal Logic Synthesis Format (TLSF), a high-level format to describe synthesis problems via Linear Temporal Logic (LTL). The format builds upon standard LTL, but additionally allows to use high-level constructs, such as…

Logic in Computer Science · Computer Science 2016-11-24 Swen Jacobs , Felix Klein , Sebastian Schirmer
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