Synergistic Synthesis of Ranking Functions and Invariants for Efficient Termination Analysis

核心概念

Syndicate is a novel framework that synergistically guides the search for both ranking functions and invariants to efficiently prove the termination of complex programs with arbitrarily nested loops, disjunctive conditionals, and non-linear statements.

要約

The content discusses a novel framework called Syndicate for efficient termination analysis of complex programs. The key insights are:

Existing techniques either synthesize invariants and ranking functions independently or combine them into a single query, both of which are inefficient. Syndicate proposes a synergistic approach where the search for ranking functions and invariants guide each other.

For a single loop, Syndicate maintains an under-approximation of the reachable states (set 𝑟) and an over-approximation of the reachable states (invariant I). It iteratively generates a candidate ranking function, checks its validity using the invariant, and refines the invariant or the set of reachable states based on the counter-examples.

For programs with nested loops, Syndicate maintains an under-approximation of the transition relation (set 𝑡) and over-approximations of the reachable states for each loop (invariants I𝑜, I𝑖). The search for ranking functions and invariants are synergistically guided across the nested loops.

Syndicate is parameterized by a set of possible invariants I and a set of possible ranking functions F. Under computability assumptions and assumptions on the structure of I and F, Syndicate is guaranteed to be relatively complete: if there exists a termination proof using the invariants in I and ranking functions in F, then Syndicate will find it.

Syndicate outperforms state-of-the-art termination analysis tools both in the number of benchmarks proved and in the average time taken. It can also prove some benchmarks that none of the existing tools can.

統計

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引用

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抽出されたキーインサイト

Syndicate

by Yasmin Sarit... 場所 arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.05951.pdf

深掘り質問

How can the synergistic search approach in Syndicate be extended to handle programs with disjunctive conditionals and non-linear statements

The synergistic search approach in Syndicate can be extended to handle programs with disjunctive conditionals and non-linear statements by incorporating more complex templates for invariants and ranking functions. For disjunctive conditionals, the search can involve generating multiple candidate invariants or ranking functions based on the different branches of the conditional. The synergistic approach can guide the search by exchanging information between the different branches to refine the templates effectively.
When it comes to non-linear statements, the search can involve more intricate calculations and constraints in the templates. The synergistic search can adapt by exploring a wider range of possibilities for ranking functions and invariants that can handle the non-linear nature of the statements. By leveraging the synergy between the searches, the algorithm can efficiently navigate the search space to find valid termination proofs for programs with disjunctive conditionals and non-linear statements.

Can the completeness guarantees of Syndicate be strengthened by relaxing the assumptions on the structure of the invariant and ranking function templates

The completeness guarantees of Syndicate can potentially be strengthened by relaxing the assumptions on the structure of the invariant and ranking function templates. One way to enhance completeness is to allow for more flexible templates that can capture a broader range of properties and behaviors in programs. By expanding the templates to accommodate a wider variety of invariants and ranking functions, Syndicate can increase its capability to find valid termination proofs for a larger set of programs.
Additionally, relaxing the assumptions on the structure of the templates can involve incorporating more sophisticated techniques for template generation and refinement. This can include adaptive template learning algorithms that adjust the templates based on the characteristics of the program being analyzed. By dynamically adapting the templates during the search process, Syndicate can improve its completeness by exploring a more diverse set of possibilities for invariants and ranking functions.

What are the potential applications of the synergistic synthesis technique beyond termination analysis, such as in other program verification tasks or in the broader field of program synthesis

The synergistic synthesis technique employed in Syndicate has potential applications beyond termination analysis in program verification tasks and program synthesis.

Program Verification: The synergistic approach can be applied to various program verification tasks such as safety analysis, security analysis, and correctness verification. By guiding the search for properties and invariants that prove specific properties of programs, Syndicate can enhance the efficiency and effectiveness of program verification processes.

Program Synthesis: The synergistic synthesis technique can also be utilized in program synthesis tasks where the goal is to automatically generate programs that satisfy certain specifications. By guiding the search for suitable program structures and properties, Syndicate can assist in synthesizing programs that meet desired requirements.

Optimization: The synergistic approach can be adapted for optimization tasks in program analysis, where the goal is to improve the performance or efficiency of programs. By guiding the search for optimizations based on ranking functions and invariants, Syndicate can help identify opportunities for enhancing program behavior.

Overall, the synergistic synthesis technique in Syndicate has the potential to be a versatile tool in various program analysis and synthesis domains, offering benefits in terms of efficiency, completeness, and accuracy.