Three Simulation Algorithms for Labelled Transition Systems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2013

## Three Simulation Algorithms for Labelled Transition Systems

Gérard Cécé
• Function : Correspondent author
• PersonId : 934969

Connectez-vous pour contacter l'auteur

#### Abstract

Algorithms which compute the coarsest simulation preorder are generally designed on Kripke structures. Only in a second time they are extended to labelled transition systems. By doing this, the size of the alphabet appears in general as a multiplicative factor to both time and space complexities. Let $Q$ denotes the state space, $\rightarrow$ the transition relation, $\Sigma$ the alphabet and $P_{sim}$ the partition of $Q$ induced by the coarsest simulation equivalence. In this paper, we propose a base algorithm which minimizes, since the first stages of its design, the incidence of the size of the alphabet in both time and space complexities. This base algorithm, inspired by the one of Paige and Tarjan in 1987 for bisimulation and the one of Ranzato and Tapparo in 2010 for simulation, is then derived in three versions. One of them has the best bit space complexity up to now, $O(|P_{sim}|^2+|{\rightarrow}|.\log|{\rightarrow}|)$, while another one has the best time complexity up to now, $O(|P_{sim}|.|{\rightarrow}|)$. Note the absence of the alphabet in these complexities. A third version happens to be a nice compromise between space and time since it runs in $O(b.|P_{sim}|.|{\rightarrow}|)$ time, with $b$ a branching factor generally far below $|P_{sim}|$, and uses $O(|P_{sim}|^2.\log|P_{sim}|+|{\rightarrow}|.\log|{\rightarrow}|)$ bits.

#### Domains

Formal Languages and Automata Theory [cs.FL]

### Dates and versions

hal-00771518 , version 1 (08-01-2013)

### Identifiers

• HAL Id : hal-00771518 , version 1
• ARXIV :

### Cite

Gérard Cécé. Three Simulation Algorithms for Labelled Transition Systems. 2013. ⟨hal-00771518⟩

### Export

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

106 View