## Reachability Problems: 4th International Workshop, RP 2010, Brno, Czech Republic, August 28-29, 2010. ProceedingsThis volume contains the papers presented at the 4th International Workshop on Reachability Problems, RP 2010 held during August 28–29, 2010 in the F- ulty of Informatics, Masaryk University, Brno, Czech Republic and co-located with Joint MFCS and CSL 2010 (35th InternationalSymposiums on Mathem- ical Foundations of Computer Science and 19th EACSL Annual Conferences on Computer Science Logic). RP 2010 was the fourth in the series of workshops following three successful meetings at Ecole Polytechnique, France in 2009 at University of Liverpool, UK in 2008 and at Turku University, Finland in 2007. TheReachabilityProblemsworkshopsseriesaimsatgatheringtogethersch- ars from diverse disciplines and backgrounds interested in reachability problems that appearin algebraicstructures,computationalmodels, hybridsystems, logic and veri?cation, etc. Reachability is a fundamental problem in the context of many models and abstractions which describe various computational processes. Analysisofthecomputationaltracesandpredictabilityquestionsforsuchmodels can be formalized as a set of di?erent reachability problems. In general, reac- bility can be formulated as follows: Given a computational system with a set of allowed transformations (functions), decide whether a certain state of a system is reachable from a given initial state by a set of allowed transformations. The same questions can be asked not only about reachability of exact states of the system but also about a set of states expressed in terms of some property as a parameterized reachability problem. Another set of predictability questions can be seen in terms of reachability of eligible traces of computations,unavoidability ofsomedynamicsandapossibilitytoavoidundesirabledynamicsusingalimited control. |

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### Contents

Descriptional Complexity of Unambiguous Finite State Machines and Pushdown Automata | 1 |

Symbolic and Compositional Reachability for Timed Automata | 24 |

Temporal Logics over Linear Time Domains Are in PSPACE | 29 |

Lossy Counter Machines Decidability Cheat Sheet | 51 |

Behavioral Cartography of Timed Automata | 76 |

On the Joint Spectral Radius for Bounded Matrix Languages | 91 |

ZReachability Problem for Games on 2Dimensional Vector Addition Systems with States Is in P | 104 |

Towards the Frontier between Decidability and Undecidability for Hyperbolic Cellular Automata | 120 |

Rewriting Systems for Reachability in Vector Addition Systems with Pairs | 133 |

The Complexity of Model Checking for Intuitionistic Logics and Their Modal Companions | 146 |

Depth Boundedness in Multiset Rewriting Systems with Name Binding | 161 |

Efficient Construction of Semilinear Representations of Languages Accepted by Unary NFA | 176 |

Efficient Graph Reachability Query Answering Using Tree Decomposition | 183 |

198 | |

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### Common terms and phrases

algorithm ambiguity AsAgap cellular automaton chains complexity Computer Science conﬁgurations consider Corollary cycles from A=R decidable Dedekind-complete deﬁnable deﬁned deﬁnition denoted depth-bounded deterministic diﬀerent DPDAs edges equivalent exponential EXPTIME finite ﬁnite automata ﬁnite set ﬁrst ﬁrst-order ﬁxed formal power series formula fragment given Heidelberg heptagrid iﬀ inﬁnite intuitionistic logic Lemma linear orders LNCS lossy counter machines lower bounds modal logic model checking model checking problem monadic multiset n-state node nondeterminism NPDA obtained P-complete pairs parameters pentagrid Petri nets polynomial probabilistic proof properties propositional logic pspace pushdown automata reachability problem reduction resp rewriting system rule satisﬁability problem semantics sequence simple path simulation space spectral radius Springer strategy structure subset suﬃcient temporal logic Theorem tiles trade-oﬀ transitive tree decomposition unary languages unary NFA undecidable upper bound valuation variables VASP VASS veriﬁcation vertex vertices