Implicit Rankings for Verifying Liveness Properties in First-Order Logic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916530974883840 |
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| author | Lotan, Raz Shoham, Sharon |
| author_facet | Lotan, Raz Shoham, Sharon |
| contents | Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural ranking functions is beyond reach of existing solvers. To address this, we introduce the notion of implicit rankings - first-order formulas that soundly approximate the reduction of some ranking function without defining it explicitly. We provide recursive constructors of implicit rankings that can be instantiated and composed to induce a rich family of implicit rankings. Our constructors use quantifiers to approximate reasoning about useful primitives such as cardinalities of sets and unbounded sums that are not directly expressible in first-order logic. We demonstrate the effectiveness of our implicit rankings by verifying liveness properties of several intricate examples, including Dijkstra's k-state, 4-state and 3-state self-stabilizing protocols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Implicit Rankings for Verifying Liveness Properties in First-Order Logic Lotan, Raz Shoham, Sharon Logic in Computer Science Programming Languages F.3.1; I.2.2 Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural ranking functions is beyond reach of existing solvers. To address this, we introduce the notion of implicit rankings - first-order formulas that soundly approximate the reduction of some ranking function without defining it explicitly. We provide recursive constructors of implicit rankings that can be instantiated and composed to induce a rich family of implicit rankings. Our constructors use quantifiers to approximate reasoning about useful primitives such as cardinalities of sets and unbounded sums that are not directly expressible in first-order logic. We demonstrate the effectiveness of our implicit rankings by verifying liveness properties of several intricate examples, including Dijkstra's k-state, 4-state and 3-state self-stabilizing protocols. |
| title | Implicit Rankings for Verifying Liveness Properties in First-Order Logic |
| topic | Logic in Computer Science Programming Languages F.3.1; I.2.2 |
| url | https://arxiv.org/abs/2412.13996 |