# The GRAT Tool Chain - Efficient (UN)SAT Certificate Checking with Formal Correctness Guarantees

@inproceedings{Lammich2017TheGT, title={The GRAT Tool Chain - Efficient (UN)SAT Certificate Checking with Formal Correctness Guarantees}, author={Peter Lammich}, booktitle={SAT}, year={2017} }

We present the GRAT tool chain, which provides an efficient and formally verified SAT and UNSAT certificate checker. It utilizes a two phase approach: The highly optimized gratgen tool converts a DRAT certificate to a GRAT certificate, which is then checked by the formally verified gratchk tool.

## 19 Citations

### Efficient Verified (UN)SAT Certificate Checking

- Computer Science, MathematicsJournal of Automated Reasoning
- 2019

This paper presents the first SAT solver certificate checker that is formally verified down to the integer sequence representing the formula, and is even faster than the unverified state-of-the-art tool drat-trim, on a realistic set of benchmarks drawn from the 2016 and 2017 SAT competitions.

### The Proof Checkers Pacheck and Pastèque for the Practical Algebraic Calculus

- Computer Science, Mathematics2020 Formal Methods in Computer Aided Design (FMCAD)
- 2020

The checker Pacheck checks algebraic proofs more efficiently than PastÈque, but the latter is formally verified using the proof assistant Isabelle/HOL, and extension rules to simulate essential rewriting techniques required in practice are introduced.

### A verified SAT solver with watched literals using imperative HOL

- Computer ScienceCPP
- 2018

The CDCL calculus is refined to add a crucial optimization: two watched literals, and the data structure and the invariants are formalized, leading to an executable SAT solver that offers acceptable performance for some applications.

### A Verified First-Order Prover Based on Ordered Resolution

- Computer Science
- 2018

This work specifies, using the Isabelle/HOL proof assistant, a purely functional ordered resolution prover and formally establish its soundness and completeness and applies stepwise refinement to obtain, from an abstract specification of a nondeterministic prover, a verified deterministic program, written in a subset of Isabelle /HOL from which it can extract purely functional Standard ML code.

### A verified prover based on ordered resolution

- Computer Science, MathematicsCPP
- 2019

This work specifies, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establishes its soundness and refutational completeness, and applies stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program.

### Practical algebraic calculus and Nullstellensatz with the checkers Pacheck and Pastèque and Nuss-Checker

- Mathematics, Computer ScienceFormal Methods in System Design
- 2022

The practical algebraic calculus is presented as an instantiation of the polynomial calculus that can be checked efficiently and extension rules to simulate essential rewriting techniques required in practice are introduced.

### A Verified Automatic Prover Based on Ordered Resolution

- Computer Science
- 2018

This work specifies, using the Isabelle/HOL proof assistant, a purely functional ordered resolution prover and formally establishes its soundness and refutational completeness, and extracts purely functional Standard ML code that constitutes a semidecision procedure for first-order logic.

### Formalization of logical calculi in Isabelle/HOL

- Computer Science
- 2020

A formal framework for propositional satifisfiability with the conflict-driven clause learning (CDCL) procedure using the Isabelle/HOL proof assistant is developed and the inclusion of rules for forget and restart and the refinement approach are included.

### Formally Verified SAT-Based AI Planning

- Computer ScienceArXiv
- 2020

An executable formally verified SAT encoding of classical AI planning is presented, using the theorem prover Isabelle/HOL to perform the verification and it is experimentally test and shown that it can be used for reasonably sized standard planning benchmarks.

### Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

- Computer ScienceCPP
- 2019

This paper describes and reflects on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order logic.

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This paper presents the first SAT solver certificate checker that is formally verified down to the integer sequence representing the formula, and is even faster than the unverified state-of-the-art tool drat-trim, on a realistic set of benchmarks drawn from the 2016 and 2017 SAT competitions.

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