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30
HigherOrder Pushdown Trees Are Easy
, 2002
"... We show that the monadic secondorder theory of an infinite tree recognized by a higherorder pushdown automaton of any level is decidable. We also show that trees recognized by pushdown automata of level n coincide with trees generated by safe higherorder grammars of level n. Our decidability resu ..."
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Cited by 43 (2 self)
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We show that the monadic secondorder theory of an infinite tree recognized by a higherorder pushdown automaton of any level is decidable. We also show that trees recognized by pushdown automata of level n coincide with trees generated by safe higherorder grammars of level n. Our decidability result extends the result of Courcelle on algebraic (pushdown of level 1) trees and our own result on trees of level 2.
PrefixRecognisable Graphs and Monadic SecondOrder Logic
, 2001
"... We present several characterisations of the class of prefixrecognisable ..."
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Cited by 20 (1 self)
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We present several characterisations of the class of prefixrecognisable
Pushdown Specifications
, 2002
"... Traditionally, model checking is applied to finitestate systems and regular specifications. While researchers have successfully extended the applicability of model checking to infinitestate systems, almost all existing work still consider regular specification formalisms. There are, however, ma ..."
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Cited by 18 (5 self)
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Traditionally, model checking is applied to finitestate systems and regular specifications. While researchers have successfully extended the applicability of model checking to infinitestate systems, almost all existing work still consider regular specification formalisms. There are, however, many interesting nonregular properties one would like to model check.
Parity games played on transition graphs of onecounter processes
 In FoSSaCS
, 2006
"... Abstract. We consider parity games played on special pushdown graphs, namely those generated by onecounter processes. For parity games on pushdown graphs, it is known from [23] that deciding the winner is an ExpTimecomplete problem. An important corollary of this result is that the µcalculus mode ..."
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Cited by 14 (0 self)
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Abstract. We consider parity games played on special pushdown graphs, namely those generated by onecounter processes. For parity games on pushdown graphs, it is known from [23] that deciding the winner is an ExpTimecomplete problem. An important corollary of this result is that the µcalculus model checking problem for pushdown processes is ExpTimecomplete. As onecounter processes are special cases of pushdown processes, it follows that deciding the winner in a parity game played on the transition graph of a onecounter process can be achieved in ExpTime. Nevertheless the proof for the ExpTimehardness lower bound of [23] cannot be adapted to that case. Therefore, a natural question is whether the ExpTime upper bound can be improved in this special case. In this paper, we adapt techniques from [11, 4] and provide a PSpace upper bound and a DPhard lower bound for this problem. We also give two important consequences of this result. First, we improve the best upper bound known for modelchecking onecounter processes against µcalculus. Second, we show how these games can be used to solve pushdown games with winning conditions that are Boolean combinations of a parity condition on the control states with conditions on the stack height. 1
Uniform solution of parity games on prefixrecognizable graphs
 ENTCS
, 2002
"... Walukiewicz gave in 1996 a solution for parity games on pushdown graphs: he proved the existence of pushdown strategies and determined the winner with an EXPTIME procedure. We give a new presentation and a new algorithmic proof of these results, obtain a uniform solution for parity games (independe ..."
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Cited by 14 (0 self)
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Walukiewicz gave in 1996 a solution for parity games on pushdown graphs: he proved the existence of pushdown strategies and determined the winner with an EXPTIME procedure. We give a new presentation and a new algorithmic proof of these results, obtain a uniform solution for parity games (independent of their initial configuration), and extend the results to prefixrecognizable graphs. The winning regions of the players are proved to be effectively regular, and winning strategies are computed. 1
Deciding Monadic Theories of Hyperalgebraic Trees
"... We show that the monadic secondorder theory of any infinite tree generated by a higherorder grammar of level 2 subject to a certain syntactic restriction is decidable. By this we extend the result of Courcelle [7] that the MSO theory of a tree generated by a grammar of level 1 (algebraic) is decid ..."
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Cited by 12 (4 self)
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We show that the monadic secondorder theory of any infinite tree generated by a higherorder grammar of level 2 subject to a certain syntactic restriction is decidable. By this we extend the result of Courcelle [7] that the MSO theory of a tree generated by a grammar of level 1 (algebraic) is decidable. To this end, we develop a technique of representing infinite trees by infinite lambda terms, in such a way that the MSO theory of a tree can be interpreted in the MSO theory of a lambda term.
A finite semantics of simplytyped lambda terms for infinite runs of automata
 Procedings of the 20th international Workshop on Computer Science Logic (CSL ’06), volume 4207 of Lecture Notes in Computer Science
, 2006
"... Vol. 3 (3:1) 2007, pp. 1–23 ..."
Modular strategies for infinite games on recursive game graphs
 In Proceedings of CAV’03, volume 2725 of LNCS
, 2003
"... ..."
Global modelchecking of infinitestate systems
 in: Proc. 16th International Conference on Computer Aided Verification, CAV’04, in: LNCS
, 2004
"... Abstract. We extend the automatatheoretic framework for reasoning about infinitestate sequential systems to handle also the global modelchecking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed a ..."
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Cited by 8 (0 self)
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Abstract. We extend the automatatheoretic framework for reasoning about infinitestate sequential systems to handle also the global modelchecking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finitestate automata. Checking that the system satisfies a temporal property can then be done by a twoway automaton that navigates through the tree. The framework is known for local model checking. For branching time properties, the framework uses twoway alternating automata. For linear time properties, the framework uses twoway path automata. In order to solve the global modelchecking problem we show that for both types of automata, given a regular tree, we can construct a nondeterministic word automaton that accepts all the nodes in the tree from which an accepting run of the automaton can start. 1
Axiomatising Treeinterpretable Structures
 IN PROC. 19TH INT. SYMP. ON THEORETICAL ASPECTS OF COMPUTER SCIENCE, LNCS 2285, 2002
, 2001
"... We introduce the class of treeinterpretable structures which generalises the notion of a prefixrecognisable graph to arbitrary relational structures. We prove that every treeinterpretable structure is finitely axiomatisable in guarded secondorder logic with cardinality quantifiers. ..."
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Cited by 8 (0 self)
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We introduce the class of treeinterpretable structures which generalises the notion of a prefixrecognisable graph to arbitrary relational structures. We prove that every treeinterpretable structure is finitely axiomatisable in guarded secondorder logic with cardinality quantifiers.