Towards efficient verification of population protocols

Area of Science:

• Theoretical Computer Science
• Distributed Computing
• Formal Verification

Background:

• Population protocols model computation using anonymous, identical finite-state agents.
• The well-specification problem, determining if a protocol guarantees consensus from all initial configurations, is known to be highly complex.
• Previous work established decidability but with TOWER-hard complexity, lacking efficient verification methods.

Purpose of the Study:

• To introduce a new class of protocols, well-specified strongly-silent protocols ($$), suitable for automatic verification.
• To demonstrate that $$ protocols possess the same computational power as general well-specified protocols.
• To develop the first software capable of automatically proving correctness for infinitely many inputs of $$ protocols.

Main Methods:

• Introduction of the class $$ of well-specified strongly-silent protocols.
• Mathematical proof of the equivalence in computational power between $$ and general well-specified protocols.
• Reduction of membership and correctness problems for $$ to solving boolean combinations of linear constraints over $$.

Main Results:

• The class $$ is suitable for automatic verification.
• $$ protocols capture standard protocols found in the literature.
• The study presents the first software tool for automatically verifying correctness across all possible inputs for $$ protocols.

Conclusions:

• The proposed $$ protocols offer a practical approach to verifying complex computational systems.
• Automatic verification of population protocols is now feasible for a significant class of protocols.
• This work bridges the gap between theoretical models of computation and practical verification tools.