## Analysis of Recursive State Machines (2001)

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Venue: | In Proceedings of CAV 2001 |

Citations: | 110 - 21 self |

### BibTeX

@INPROCEEDINGS{Alur01analysisof,

author = {Rajeev Alur and Kousha Etessami and Mihalis Yannakakis},

title = {Analysis of Recursive State Machines},

booktitle = {In Proceedings of CAV 2001},

year = {2001},

pages = {207--220},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

. Recursive state machines (RSMs) enhance the power of ordinary state machines by allowing vertices to correspond either to ordinary states or to potentially recursive invocations of other state machines. RSMs can model the control flow in sequential imperative programs containing recursive procedure calls. They can be viewed as a visual notation extending Statecharts-like hierarchical state machines, where concurrency is disallowed but recursion is allowed. They are also related to various models of pushdown systems studied in the verification and program analysis communities. After introducing RSMs, we focus on whether state-space analysis can be performed efficiently for RSMs. We consider the two central problems for algorithmic analysis and model checking, namely, reachability (is a target state reachable from initial states) and cycle detection (is there a reachable cycle containing an accepting state). We show that both these problems can be solved in time O(n` 2 ) and space O(n`), where n is the size of the recursive machine and ` is the maximum, over all component state machines, of the minimum of the number of entries and the number of exits of each component. We also study the precise relationship between RSMs and closely related models. 1

### Citations

2123 | Statecharts: A Visual Formalism for Complex Systemsâ€ť; Sci
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- 1987
(Show Context)
Citation Context ...cal sequential imperative programming languages with recursive procedure calls. Alternatively, RSMs can be viewed as a variant of visual notations for hierarchical state machines, such as Statecharts =-=[10]-=- and UML [5], where concurrency is disallowed but recursion is allowed. More precisely, a recursive state machine consists of a set of component machines. Each component has a set of nodes (atomic sta... |

2008 |
The Unified Modeling Language User Guide
- Booch, Rumbaugh, et al.
- 2005
(Show Context)
Citation Context ...l imperative programming languages with recursive procedure calls. Alternatively, RSMs can be viewed as a variant of visual notations for hierarchical state machines, such as Statecharts [10] and UML =-=[5]-=-, where concurrency is disallowed but recursion is allowed. More precisely, a recursive state machine consists of a set of component machines. Each component has a set of nodes (atomic states) and box... |

1064 |
Principles of Database and Knowledge-Base Systems. Volume II: The New Technologies
- Ullman
- 1989
(Show Context)
Citation Context ...s: R i (x; y) holds iff there is a path in TA from hxi to hyi. The predicates R i (x; y) are determined by a series of simple recursive relationships which we will write in the style of Datalog rules =-=[13]-=-. Recall some terminology. An atom is a term P () where P is a predicate (relation) symbol andsis a tuple of appropriate arity consisting of variables and constants from appropriate domains. A ground ... |

369 | Precise interprocedural dataflow analysis via graph reachability
- Reps, Horwitz, et al.
- 1995
(Show Context)
Citation Context ...erlying global state-space is infinite and behaves like a pushdown system. While RSMs are closely related to pushdown systems, which are studied in verification and program analysis in many disguises =-=[12, 6]-=-, RSMs appear to be the appropriate definition for visual modeling and allow tigher analysis. We study the two most fundamental questions for model checking of safety and liveness properties, respecti... |

289 | Reachability Analysis of Pushdown Automata: Application to ModelChecking
- Bouajjani, Esparza, et al.
- 1997
(Show Context)
Citation Context ...erlying global state-space is infinite and behaves like a pushdown system. While RSMs are closely related to pushdown systems, which are studied in verification and program analysis in many disguises =-=[12, 6]-=-, RSMs appear to be the appropriate definition for visual modeling and allow tigher analysis. We study the two most fundamental questions for model checking of safety and liveness properties, respecti... |

218 | Bebop: A Symbolic Model Checker for Boolean Programs
- Ball, Rajamani
(Show Context)
Citation Context ...ut that by working with RSMs directly we can achieve better bounds in terms of `. Ball and Rajamani consider the model of Boolean programs, which can be viewed as RSMs extended with boolean variables =-=[3]-=-. They have implemented a BDD-based symbolic model checker that solves the reachability problem for Boolean programs. The main technique is to compute the summary of the inputoutput relation of a proc... |

146 | Efficient algorithms for model checking pushdown systems
- Esparza, Hansel, et al.
- 2000
(Show Context)
Citation Context ...cal machines can not be applied to RSMs. RSMs are closely related to pushdown systems. Model checking of pushdown systems has been studied extensively for both linear- and branching-time requirements =-=[6, 7, 9, 8]-=-. These algorithms are based on an automata-theoretic approach. Each configuration is viewed as a string over stack symbols, and the reachable configurations are shown to be a regular set that can be ... |

119 | Program analysis via graph reachability
- Reps
- 1998
(Show Context)
Citation Context ...equires O(n 3 ) time. Using fast matrix multiplication, Valiant [14] was able to slightly improve the asymptotic bound, but his algorithm is highly impractical. A related problem is CFL-reachability (=-=[15, 11]-=-), where for a fixed grammar G, we are given a directed, edge-labeled, graph H , having size n, with designated source and target nodes s and t, and we wish to determine whether s can reach t in H via... |

112 | A direct symbolic approach to model checking pushdown systems
- Finkel, Willems, et al.
- 1997
(Show Context)
Citation Context ...cal machines can not be applied to RSMs. RSMs are closely related to pushdown systems. Model checking of pushdown systems has been studied extensively for both linear- and branching-time requirements =-=[6, 7, 9, 8]-=-. These algorithms are based on an automata-theoretic approach. Each configuration is viewed as a string over stack symbols, and the reachable configurations are shown to be a regular set that can be ... |

81 |
Model checking and boolean graphs
- Andersen
- 1994
(Show Context)
Citation Context ...uch that p 0 is reachable, or (c) p is a -vertex and for 8p 0 such that (p 0 ; p) 2 E, p 0 is reachable. It is well-known that reachability in AND-OR graphs can be computed in linear time (see, e.g., =-=[2]-=-). We can define from the rules an AND-OR graph GA with one -vertex for each ground atom R i (x; y) and one -vertex for each instantiated body of a rule with two conjuncts, i.e., rule of type 3. The s... |

78 | Model checking of hierarchical state machines
- Alur, Yannakakis
- 1998
(Show Context)
Citation Context ...uchi automata, via a product construction for Buchi automata with RSMs. Related work. Our definition of recursive state machines naturally generalizes the definition of hierarchical state machines of =-=[1]-=-. For hierarchical state machines, the underlying state-space is guaranteed to be finite, but can be exponential in the size of the original machine. Algorithms for analysis of hierarchical state mach... |

62 |
General Context-Free Recognition in Less than Cubic Time
- Valiant
- 1975
(Show Context)
Citation Context ...ee grammar G, and given a string w of length n, we wish to determine if G can generate w. The classic C-K-Y algorithm for this problem requires O(n 3 ) time. Using fast matrix multiplication, Valiant =-=[14]-=- was able to slightly improve the asymptotic bound, but his algorithm is highly impractical. A related problem is CFL-reachability ([15, 11]), where for a fixed grammar G, we are given a directed, edg... |

55 |
Graph Theoretic Methods in Database Theory
- Yannakakis
- 1990
(Show Context)
Citation Context ...equires O(n 3 ) time. Using fast matrix multiplication, Valiant [14] was able to slightly improve the asymptotic bound, but his algorithm is highly impractical. A related problem is CFL-reachability (=-=[15, 11]-=-), where for a fixed grammar G, we are given a directed, edge-labeled, graph H , having size n, with designated source and target nodes s and t, and we wish to determine whether s can reach t in H via... |

43 | Model checking of unrestricted hierarchical state machines
- Benedikt, Godefroid, et al.
- 2001
(Show Context)
Citation Context ... call stack" or "unbounded call stack". This distinction had not been considered in all previous papers. Note: Results similar to ours have been obtained independently, and submitted co=-=ncurrently, by [4]-=- on a model identical to RSMs. 2 Recursive State Machines Syntax. A recursive state machine (RSM) A over a finite alphabet \Sigma is given by a tuple hA 1 ; : : : ; A k i, where each component state m... |

37 | B.: Model checking the full modal mu-calculus for infinite sequential processes
- Burkart, Steffen
- 1997
(Show Context)
Citation Context ...cal machines can not be applied to RSMs. RSMs are closely related to pushdown systems. Model checking of pushdown systems has been studied extensively for both linear- and branching-time requirements =-=[6, 7, 9, 8]-=-. These algorithms are based on an automata-theoretic approach. Each configuration is viewed as a string over stack symbols, and the reachable configurations are shown to be a regular set that can be ... |