[Paper Review] Quantifier Elimination for Database Driven Verification

Diego Calvanese, Silvio Ghilardi+3 more|arXiv (Cornell University)|Jun 25, 2018

Advanced Database Systems and Queries41 references6 citations

TL;DR

This paper introduces a novel approach to database-driven verification by leveraging quantifier elimination through covers, which are shown to be equivalent to model completions in model theory. The authors present a constrained Superposition Calculus for tractable cover computation in the EUF (Equality with Uninterpreted Functions) fragment, demonstrating efficiency via experiments with the mcmt tool on real-world BPMN workflows.

ABSTRACT

Running verification tasks in database driven systems requires solving quantifier elimination problems of a new kind. These quantifier elimination problems are related to the notion of a cover introduced in ESOP 2008 by Gulwani and Musuvathi. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus, equipped with appropriate settings and reduction strategies. In addition, we show that cover computations are computationally tractable for the fragment of the language used in applications to database driven verification. This observation is confirmed by analyzing the preliminary results obtained using the MCMT tool on the verification of data-aware process benchmarks. These benchmarks can be found in the last version of the tool distribution.

Motivation & Objective

• Address the challenge of precise reachable state computation in infinite-state systems with data-aware processes.
• Overcome the computational intractability of quantifier elimination in database-driven verification by introducing covers as a tractable alternative.
• Establish a formal connection between covers and model completions in model theory to unify concepts across logic and verification.
• Develop an efficient, optimized procedure for cover computation in the EUF fragment with unary functions and relations, enabling practical verification.
• Integrate the method into the mcmt model checker to support automated verification of real-world data-aware process models.

Proposed method

• Formalize covers as equivalent to quantifier elimination in model completions, linking database verification to model theory.
• Design a constrained version of the Superposition Calculus with tailored settings and reduction strategies for cover computation.
• Prove completeness of the constrained Superposition Calculus for computing covers in the EUF fragment.
• Implement the method in the mcmt tool, using Knuth-Bendix completion for ground literals in EUF with unary functions and relations.
• Extend the implementation to handle axioms involving undefined values (e.g., $e_j \neq \text{undef}$) by propagating constraints through function applications.
• Integrate the approach into a backward search algorithm for model checking, ensuring soundness and efficiency in practice.

Experimental results

Research questions

• RQ1 How can covers be used as a computationally tractable alternative to full quantifier elimination in database-driven verification?
• RQ2 What is the formal relationship between covers and model completions in model theory?
• RQ3 Can the Superposition Calculus be adapted with constraints and reduction strategies to compute covers efficiently?
• RQ4 What are the complexity bounds for cover computation in the EUF fragment with unary functions and relations?
• RQ5 To what extent can the proposed method scale to real-world data-aware process models, such as BPMN workflows?

Key findings

• Covers are formally equivalent to quantifier elimination in model completions, establishing a foundational link between model theory and verification.
• Cover computation is computationally tractable for the EUF fragment with unary functions and relations, enabling efficient verification.
• The mcmt tool successfully computes covers for all 32 real-world BPMN workflow benchmarks in seconds, with cover generation occurring instantaneously during model checking.
• The implementation uses a lightweight extension of Knuth-Bendix completion for ground literals, effectively handling constraints involving undefined values.
• The method supports practical verification of data-aware processes, including those with first-order and higher-order variables.
• The approach is extensible to combined theories and future work aims at integrating symbol elimination and richer data types.