# A Complete Decision Procedure for Linearly Compositional Separation Logic with Data Constraints

@inproceedings{Gu2016ACD, title={A Complete Decision Procedure for Linearly Compositional Separation Logic with Data Constraints}, author={Xincai Gu and Taolue Chen and Zhilin Wu}, booktitle={IJCAR}, year={2016} }

Separation logic is a widely adopted formalism to verify programs manipulating dynamic data structures. Entailment checking of separation logic constitutes a crucial step for the verification of such programs. In general this problem is undecidable, hence only incomplete decision procedures are provided in most state-of-the-art tools. In this paper, we define a linearly compositional fragment of separation logic with inductive definitions, where traditional shape properties for linear data…

## 19 Citations

### Satisfiability of Compositional Separation Logic with Tree Predicates and Data Constraints

- Computer ScienceCADE
- 2017

This paper shows that the satisfiability problem of CSLTP is decidable, and proposes compositional separation logic with tree predicates (CSLTP), where properties such as sortedness and height-balancedness of complex data structures can be fully specified.

### Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

- Computer ScienceSOFSEM
- 2019

A crucial step of the decision procedure is to compute the transitive closure of DBS-definable set relations, to capture which the satisfiability of RQSPA is shown to be decidable by harnessing advanced automata-theoretic techniques.

### Compositional Satisfiability Solving in Separation Logic

- Computer ScienceVMCAI
- 2021

A novel decision procedure to the satisﬁability problem in array separation logic combined with general inductive predicates and arithmetic is introduced and an expressive decidable fragment for the compositionality is identified.

### Compositional entailment checking for a fragment of separation logic

- Computer ScienceAPLAS
- 2014

We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds…

### Completeness of Cyclic Entailment Proofs in Separation Logic with Inductive Predicates and Arithmetic (Technical Report)

- Computer Science, Philosophy
- 2019

This work considers a decision procedure that could deduce linear validity proofs (i.e., without back-tracking) for the quantifier-free entailment problem and presents a sound, complete and terminating cyclic proof system for the problem in separation logic combining with linearly inductive predicates and arithmetic properties.

### A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic

- Computer Science, MathematicsCAV
- 2017

This work considers the satisfiability problem for a fragment of separation logic including inductive predicates with shape and arithmetic properties and proposes a decision procedure based on a novel algorithm to infer a finite representation for each inductive predicate which precisely characterises its satisfiability.

### Strong-Separation Logic

- Computer ScienceESOP
- 2021

It is argued that the resulting logic, strong-separation logic, can be used for symbolic execution and abductive reasoning just like “standard” separation logic, while remaining decidable even in the presence of both the magic wand and inductive predicates.

### Biabduction (and Related Problems) in Array Separation Logic

- Computer ScienceCADE
- 2017

This work investigates array separation logic (ASL), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of allocated memory, and shows satisfiability to be NP-complete and entailment to be decidable with high complexity.

### Frame Inference for Inductive Entailment Proofs in Separation Logic

- Computer Science, PhilosophyTACAS
- 2018

This work presents an automatic frame inference approach for an expressive fragment of separation logic and shows how to strengthen the inferred frame through predicate normalization and arithmetic inference.

### Bi-Abductive Inference for Shape and Ordering Properties

- Computer Science2019 24th International Conference on Engineering of Complex Computer Systems (ICECCS)
- 2019

This work presents a novel one-stage bi-abductive procedure for a combination of data structures and ordering values in the spirit of the Unfold-and-Match paradigm, and demonstrates that it is promising for an automated verification of heap-manipulating programs.

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