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DOI: 10.4230/LIPIcs.CONCUR.2015.383
On Reachability Analysis of Pushdown Systems with Transductions: Application to Boolean Programs with Call-by-Reference

Authors: Fu Song, Weikai Miao, Geguang Pu, and Min Zhang

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract
Pushdown systems with transductions (TrPDSs) are an extension of pushdown systems (PDSs) by associating each transition rule with a transduction, which allows to inspect and modify the stack content at each step of a transition rule. It was shown by Uezato and Minamide that TrPDSs can model PDSs with checkpoint and discrete-timed PDSs. Moreover, TrPDSs can be simulated by PDSs and the predecessor configurations pre^*(C) of a regular set C of configurations can be computed by a saturation procedure when the closure of the transductions in TrPDSs is finite. In this work, we comprehensively investigate the reachability problem of finite TrPDSs. We propose a novel saturation procedure to compute pre^*(C) for finite TrPDSs. Also, we introduce a saturation procedure to compute the successor configurations post^*(C) of a regular set C of configurations for finite TrPDSs. From these two saturation procedures, we present two efficient implementation algorithms to compute pre^*(C) and post^*(C). Finally, we show how the presence of transductions enables the modeling of Boolean programs with call-by-reference parameter passing. The TrPDS model has finite closure of transductions which results in model-checking approach for Boolean programs with call-by-reference parameter passing against safety properties.
Cite as

Fu Song, Weikai Miao, Geguang Pu, and Min Zhang. On Reachability Analysis of Pushdown Systems with Transductions: Application to Boolean Programs with Call-by-Reference. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 383-397, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{song_et_al:LIPIcs.CONCUR.2015.383,
  author =	{Song, Fu and Miao, Weikai and Pu, Geguang and Zhang, Min},
  title =	{{On Reachability Analysis of Pushdown Systems with Transductions: Application to Boolean Programs with Call-by-Reference}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{383--397},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.383},
  URN =		{urn:nbn:de:0030-drops-53624},
  doi =		{10.4230/LIPIcs.CONCUR.2015.383},
  annote =	{Keywords: Verification, Reachability problem, Pushdown system with transductions, Boolean programs with call-by-reference}
}
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