Abstract
We propose a generalization of results on the decidability of emptiness for several restricted classes of sequential and distributed automata with auxiliary storage (stacks, queues) that have recently been proved. Our generalization relies on reducing emptiness of these automata to finite-state graph automata (without storage) restricted to monadic second-order (MSO) definable graphs of bounded tree-width, where the graph structure encodes the mechanism provided by the auxiliary storage. Our results outline a uniform mechanism to derive emptiness algorithms for automata, explaining and simplifying several existing results, as well as proving new decidability results.
Supplemental Material
- R. Alur and P. Madhusudan. Visibly pushdown languages. In L. Babai, editor, STOC, pages 202--211. ACM, 2004. Google Scholar
Digital Library
- R. Alur and P. Madhusudan. Adding nesting structure to words. In O. H. Ibarra and Z. Dang, editors, Developments in Language Theory, volume 4036 of Lecture Notes in Computer Science, pages 1--13. Springer, 2006. Google Scholar
Digital Library
- R. Alur and P. Madhusudan. Adding nesting structure to words. J. ACM, 56 (3), 2009. Google Scholar
Digital Library
- R. Alur, K. Etessami, and P. Madhusudan. A temporal logic of nested calls and returns. In K. Jensen and A. Podelski, editors, TACAS, volume 2988 of Lecture Notes in Computer Science, pages 467--481. Springer, 2004.Google Scholar
- M. F. Atig. Global model checking of ordered multi-pushdown systems. In K. Lodaya and M. Mahajan, editors, Proceedings of the 30th Conference on FSTTCS, Leibniz International Proceedings in Informatics, Chennai, India, Dec. 2010. To appear.Google Scholar
- M. F. Atig, B. Bollig, and P. Habermehl. Emptiness of multi-pushdown automata is 2etime-complete. In M. Ito and M. Toyama, editors, Developments in Language Theory, volume 5257 of Lecture Notes in Computer Science, pages 121--133. Springer, 2008. Google Scholar
Digital Library
- T. Ball, R. Majumdar, T. D. Millstein, and S. K. Rajamani. Automatic predicate abstraction of C programs. In PLDI, pages 203--213, 2001. Google Scholar
Digital Library
- L. Breveglieri, A. Cherubini, C. Citrini, and S. Crespi-Reghizzi. Multi-push-down languages and grammars. Int. J. Found. Comput. Sci., 7 (3): 253--292, 1996.Google Scholar
Cross Ref
- B. Courcelle. The expression of graph properties and graph transformations in monadic second-order logic. In G. Rozenberg, editor, Handbook of Graph Grammars, pages 313--400. World Scientific, 1997. Google Scholar
Digital Library
- B. Courcelle and S. Olariu. Upper bounds to the clique width of graphs. Discrete Applied Mathematics, 101 (1--3): 77--114, 2000. Google Scholar
Digital Library
- B. Courcelle, J. A. Makowsky, and U. Rotics. Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst., 33 (2): 125--150, 2000.Google Scholar
Cross Ref
- J. Flum and M. Grohe. Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series). Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006. Google Scholar
Digital Library
- A. Heußner, J. Leroux, A. Muscholl, and G. Sutre. Reachability analysis of communicating pushdown systems. In C.-H. L. Ong, editor, FOSSACS, volume 6014 of Lecture Notes in Computer Science, pages 267--281. Springer, 2010. Google Scholar
Digital Library
- J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979. Google Scholar
Digital Library
- S. La Torre, P. Madhusudan, and G. Parlato. A robust class of context-sensitive languages. In LICS, pages 161--170. IEEE Computer Society, 2007. Google Scholar
Digital Library
- S. La Torre, P. Madhusudan, and G. Parlato. An infinite automaton characterization of double exponential time. In M. Kaminski and S. Martini, editors, CSL, volume 5213 of Lecture Notes in Computer Science, pages 33--48. Springer, 2008. Google Scholar
Digital Library
- S. La Torre, P. Madhusudan, and G. Parlato. Context-bounded analysis of concurrent queue systems. In C. R. Ramakrishnan and J. Rehof, editors, TACAS, volume 4963 of Lecture Notes in Computer Science, pages 299--314. Springer, 2008. Google Scholar
Digital Library
- S. La Torre, P. Madhusudan, and G. Parlato. Analyzing recursive programs using a fixed-point calculus. In M. Hind and A. Diwan, editors, PLDI, pages 211--222. ACM, 2009. Google Scholar
Digital Library
- S. La Torre, P. Madhusudan, and G. Parlato. Model-checking parameterized concurrent programs using linear interfaces. In T. Touili, B. Cook, and P. Jackson, editors, CAV, volume 6174 of Lecture Notes in Computer Science, pages 629--644. Springer, 2010. Google Scholar
Digital Library
- P. Madhusudan and G. Parlato. The tree width of automata with auxiliary storage. In IDEALS Technical Report http://hdl.handle.net/2142/15433, April 2010.Google Scholar
- R. Parikh. On context-free languages. J. ACM, 13 (4): 570--581, 1966. Google Scholar
Digital Library
- S. Qadeer and J. Rehof. Context-bounded model checking of concurrent software. In N. Halbwachs and L. D. Zuck, editors, TACAS, volume 3440 of Lecture Notes in Computer Science, pages 93--107. Springer, 2005. Google Scholar
Digital Library
- D. Seese. The structure of models of decidable monadic theories of graphs. Ann. Pure Appl. Logic, 53 (2): 169--195, 1991.Google Scholar
Cross Ref
- W. Thomas. On logics, tilings, and automata. In J. L. Albert, B. Monien, and M. Rodríıguez-Artalejo, editors, ICALP, volume 510 of Lecture Notes in Computer Science, pages 441--454. Springer, 1991. Google Scholar
Digital Library
Index Terms
The tree width of auxiliary storage
Recommendations
The tree width of auxiliary storage
POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languagesWe propose a generalization of results on the decidability of emptiness for several restricted classes of sequential and distributed automata with auxiliary storage (stacks, queues) that have recently been proved. Our generalization relies on reducing ...
Generalized acceptance, succinctness and supernondeterministic finite automata
Implementation and application automataWe define generalized, acceptance in nondeterministic finite automata, in order to achieve more instances of succinct descriptions of regular languages in practical applications. We show that generalized acceptance enable the construction of a hierarchy ...
Deciding Twig-definability of Node Selecting Tree Automata
Node selecting tree automata (NSTAs) constitute a general formalism defining unary queries over trees. Basically, a node is selected by an NSTA when it is visited in a selecting state during an accepting run. We consider twig patterns as an abstraction ...







Comments