# Model Checking and Transitive-Closure Logic

@inproceedings{Immerman1997ModelCA, title={Model Checking and Transitive-Closure Logic}, author={Neil Immerman and Moshe Y. Vardi}, booktitle={CAV}, year={1997} }

We give a linear-time algorithm to translate any formula from computation tree logic (CTL or CTL*) into an equivalent expression in a variable-confined fragment of transitive-closure logic FO(TC). Traditionally, CTL and CTL* have been used to express queries for model checking and then translated into μ-calculus for symbolic evaluation. Evaluation of μ-calculus formulas is, however, complete for time polynomial in the (typically huge) number of states in the Kripke structure. Thus, this is…

## 56 Citations

### Reachability Logic: An Efficient Fragment of Transitive Closure Logic

- Computer ScienceLog. J. IGPL
- 2000

We define reachability logic (RL), a fragment of FO(TC) (with boolean variables) that admits efficient model checking – linear time with a small constant – as a function of the size of the structure…

### Reducing CTL-live model checking to first-order logic validity checking

- Computer Science2014 Formal Methods in Computer-Aided Design (FMCAD)
- 2014

This paper shows that it is possible to reduce model checking of a finite or infinite Kripke structure that is expressed in F OL to a validity problem in FOL for a fragment of computational tree logic (CTL), which is called CTL-live.

### Reducing CTL-live Model Checking to Semantic Entailment in First-Order Logic ( Version 1 )

- Computer Science
- 2014

This article presents a method for reducing model checking of finite and infinite Kripke structures that are expressed in F OL to entailment checking in FOL for a fragment of computational tree logic (CTL), which it is proved that CTL-live is maximal in the sense that model Checking of CTL connectives that are not included in CTL -live is not reducible to semantic.

### Extracting Counterexamples from Transitive-Closure-Based Model Checking

- Computer Science2019 IEEE/ACM 11th International Workshop on Modelling in Software Engineering (MiSE)
- 2019

This work addresses the problem of how to extract counterexamples for the transitive-closure-based model checking (TCMC) technique by adding constraints that do not depend on the property.

### Temporal Logic Model Checking in Alloy

- Computer ScienceABZ
- 2012

This article shows how a symbolic representation of the semantics of computational tree logic with fairness constraints (CTLFC) can be written in first-order logic with the transitive closure operator, and therefore described in Alloy.

### Transitive-closure-based model checking (TCMC) in Alloy

- Computer ScienceSoftware and Systems Modeling
- 2020

This work presents transitive-closure-based model checking (TCMC), an expression of the complete model checking problem for CTLFC as a set of constraints in FOLTC without induction, iteration, or invariants, and implements it in the Alloy Analyzer.

### Improvements to Transitive-Closure-based Model Checking in Alloy

- Computer Science
- 2018

This thesis provides style guidelines for writing concise declarative models of transition systems for behavioural analysis in Alloy without any extensions to the Alloy language and compares TCMC in Alloy to NuSMV and bounded model checking in terms of modelling practices, expressibility of temporal properties, model checking results, and performance.

### Datalog LITE: a deductive query language with linear time model checking

- Computer ScienceTOCL
- 2002

Datalog LITE is a variant of Datalog that uses stratified negation, restricted variable occurrences and a limited form of universal quantification in rule bodies, and linear-time model checking algorithms for all mentioned logics are obtained in a unified way.

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