Game-Theoretic Approach to Planning and Synthesis

4-8 July 2022

  • Instructors: Giuseppe De Giacomo, Antonio Di Stasio, Giuseppe Perelli, Shufang Zhu (Sapienza University of Rome)
  • Host Institutions: Sapienza University & ICT-48 TAILOR
  • Level: Postgraduate.
  • Course duration: 20 hours.
  • Course Type: Lecture series.
  • Registration: Free but required (Please register here:
  • Class delivery modality: Blended (Online and In Presence).
  • In presence location: Room A5, Department of Computer, Automation, and Management Engineering, Sapienza University of Rome
  • Online Location: Zoom (link:
  • Schedule: From Monday 4th July to Friday 8th July from 14:00 to 18:00
  • Language: English
  • Notes: We, as instructors, will not give exams to other PhD curricula except Sapienza’s. Though we can informally discuss the topics in the course with anyone interested in them.


All the students interested in attending the course are invited to register a the following link:

Online Attendance

To attend the course online, please visit the following zoom link:


This course introduces AI planning and program synthesis for tasks (goals) expressed over finite traces instead of states. Specifically, borrowing from Formal Methods, we will consider tasks and environment specifications expressed in LTL and its finite trace variant LTLf. We will review the main results and algorithmic techniques to handle planning in nondeterministic domains. Then, we will draw connections with verification, and reactive synthesis, together with their game-theoretic solution techniques. The main catch is that working with these logics can be based on devising suitable 2-players games and finding strategies, i.e., plans, to win them. Specifically, we will cover the following topics: Planning in nondeterministic domain, Temporal Logics, LTL, LTLf, Game-theoretic Techniques, Safety Games, Reachability Games, Games for LTL/LTLf objectives, and Reactive Synthesis. This course is partially based on the work carried out in ERC Advanced Grant WhiteMech and EU ICT-48 TAILOR.

Course content

Planning: Introduction to planning and synthesis. Fixpoint calculations. Deterministic and nondeterministc domains. Planning with temporally extended goals. LTLf: linear-time temporal logic over finite traces. From LTLf o finite automata. Deterministic and nondeterministc domains with LTLf goals.

Linear Temporal Logic: Logic based language for the representation of programs. Model checking with LTL. The Synthesis problem with LTL goals. Automata-theoretic approach to Model Checking and Synthesis.

Games: Introduction to 2-player (turn-based) games on graphs and their relatioship with Planning and Synthesis. Solutions to simple objective games: Reachability, Safety, Safe-Reach, Buchi Games. Parity games: a more sophisticated game objective. Solution to parity games and their relationship with LTL synthesis.

Synthesis under environment specifications: The environment represented as an LTL specification. The synthesis under environment specifications solved as synthesis of an implication formula. Direct and more effective solutions to the synthesis under environment specifications for notable cases of LTLf formulas: Safety, Safety & Fairness, Safety & Stability, Safety & GR(1). Symbolic representation and techniques for Planning and Synthesis.


Slot 1 Slot 2
Monday 4th July Introduction to planning and synthesis, transition systems, and fixpoints (De Giacomo) Linear Temporal Logic -- LTL (Perelli)
Tuesday 5th July Planning on deterministic and nondeterministic domains (De Giacomo) LTL Model Checking and Synthesis (Perelli)
Wednesday 6th July Planning with LTLf goals (De Giacomo) Games on Graphs (Perelli)
Thursday 7th July Synthesis for LTLf goals under LTL specifications (Di Stasio) Solutions for notable cases of LTLf goals under LTL specifications (Zhu)
Friday 8th July Symbolic techniques (Zhu) Parity Games: definitions and solutions (Di Stasio)

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