Decidability of Safety Games under TSO Semantics

Core Concepts

The authors explore the decidability of safety games under Total Store Order (TSO) semantics, presenting different scenarios and strategies for player interactions.

Abstract

The content discusses the challenges posed by modern architectures on program execution models, focusing on TSO semantics. It delves into the complexity of safety games in various scenarios where players can update buffers before or after their turns. The authors provide insights into the construction of TSO games and their implications for formal verification processes.
The content also highlights the classification of TSO games into different groups based on buffer update permissions, outlining the decidability results for each group. It concludes with a detailed analysis of Group I, II, and III games, showcasing the ExpTime-completeness and undecidability in specific scenarios.
Overall, the content provides a comprehensive exploration of safety games under TSO semantics, offering valuable insights into formal verification challenges in concurrent programs.

Stats

SC is broken due to memory access optimizations.
Reachability problem decidable using alternative semantics.
Termination problem decidable using well-structured transition systems.
Robustness problem PSpace-complete.
Persistence problem PSpace-complete.
ExpTime complexity for decidable games.

Quotes

"The induced state space may be infinite even if the program itself is finite-state."
"Robustness and persistence problems are stronger than safety problem."

Key Insights Distilled From

TSO Games -- On the decidability of safety games under the total store order semantics (extended LMCS version with appendix)

by Stephan Spen... at arxiv.org 03-13-2024

https://arxiv.org/pdf/2309.02862.pdf

Deeper Inquiries

How do modern architectures impact program execution models beyond SC

Modern architectures impact program execution models beyond SC by introducing relaxations and optimizations that deviate from the traditional Sequential Consistency (SC) model. These changes can lead to unexpected behaviors in concurrent programs, even those that are correct under SC. For example, modern architectures like Intel x86 and ARM implement Total Store Order (TSO) semantics, which allow for reordering of memory accesses to improve performance. This relaxation of the execution order can result in non-deterministic behavior and challenges in verifying program correctness.

What are the implications of undecidability in safety games under TSO semantics

The implications of undecidability in safety games under TSO semantics are significant. It means that there is no algorithmic procedure that can guarantee a solution to the safety problem for these types of games. In practical terms, this means that it is impossible to determine whether a given configuration is winning for a player or not within these game structures. This poses challenges for formal verification and analysis of concurrent programs running under TSO semantics, as ensuring safety properties becomes inherently complex and potentially unachievable.

How can strategies in TSO games be optimized to improve computational complexity

Strategies in TSO games can be optimized to improve computational complexity by focusing on specific patterns or behaviors within the game structure. For example, identifying winning strategies where players have control over buffer updates at specific times can help streamline decision-making processes during gameplay. By strategically restricting certain actions or emphasizing key moves based on game dynamics, players can reduce the search space and complexity involved in determining winning configurations. Additionally, leveraging insights from previous analyses or known optimal strategies can guide players towards more efficient gameplay tactics with lower computational overhead.