Branching Temporal Logic of Calls and Returns for Pushdown Systems

• Published in: Integrated Formal Methods Vol. 11023; pp. 326 - 345
• Main Authors: Nguyen, Huu-Vu, Touili, Tayssir
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 9783319989372; 3319989375
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-98938-9_19

Pushdown Systems (PDSs) are a natural model for sequential programs with (recursive) procedure calls. In this work, we define the Branching temporal logic of CAlls and RETurns (BCARET) that allows to write branching temporal formulas while taking into account the matching between calls and returns. We consider the model-checking problem of PDSs against BCARET formulas with “standard” valuations (where an atomic proposition holds at a configuration c or not depends only on the control state of c, not on its stack) as well as regular valuations (where the set of configurations in which an atomic proposition holds is regular). We show that these problems can be effectively solved by a reduction to the emptiness problem of Alternating Büchi Pushdown Systems. We show that our results can be applied for malware detection.