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25
Visibly pushdown languages
, 2004
"... Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence i ..."
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Cited by 199 (20 self)
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Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a Vpl. We then study the problem of finding canonical minimal deterministic automata for Vpls. Though Vpls in general do not have unique minimal automata, we consider a subclass of VPAs called kmodule singleentry VPAs that correspond to programs with recursive procedures without input parameters, and show that the class of wellmatched Vpls do indeed have unique minimal kmodule singleentry automata. We also give a polynomial time algorithm that minimizes such kmodule singleentry VPAs. 1 Introduction The class of visibly pushdown languages (Vpl), introduced in [1], is a subclassof contextfree languages accepted by pushdown automata in which the input letter determines the type of operation permitted on the stack. Visibly pushdown languages are closed under all boolean operations, and problems such as inclusion, that are undecidable for contextfree languages, are decidable for Vpl. Vpls are relevant to several applications that use contextfree languages suchas the modelchecking of software programs using their pushdown models [13]. Recent work has shown applications in other contexts: in modeling semanticsof effects in processing XML streams [4], in game semantics for programming languages [5], and in identifying larger classes of pushdown specifications thatadmit decidable problems for infinite games on pushdown graphs [6].
Adding nesting structure to words
 In Developments in Language Theory, LNCS 4036
, 2006
"... We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Neste ..."
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Cited by 122 (17 self)
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We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Nested words generalize both words and ordered trees, and allow both word and tree operations. We define nested word automata—finitestate acceptors for nested words, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nested word automata are as expressive as their nondeterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene*, prefixes, and language homomorphisms; membership, emptiness, language inclusion, and language equivalence are all decidable; and definability in monadic second order logic corresponds exactly to finitestate recognizability. We also consider regular languages of infinite nested words and show that the closure properties, MSOcharacterization, and decidability of decision problems carry over. The linear encodings of nested words give the class of visibly pushdown languages of words, and this class lies between balanced languages and deterministic contextfree languages. We argue that for algorithmic verification of structured programs, instead of viewing the program as a contextfree language over words, one should view it as a regular language of nested words (or equivalently, a visibly pushdown language), and this would allow model checking of many properties (such as stack inspection, prepost conditions) that are not expressible in existing specification logics. We also study the relationship between ordered trees and nested words, and the corresponding automata: while the analysis complexity of nested word automata is the same as that of classical tree automata, they combine both bottomup and topdown traversals, and enjoy expressiveness and succinctness benefits over tree automata. 1
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 32 (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
Visibly pushdown games
 In FSTTCS 2004
, 2004
"... Abstract. The class of visibly pushdown languages has been recently defined as a subclass of contextfree languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is gi ..."
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Cited by 30 (6 self)
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Abstract. The class of visibly pushdown languages has been recently defined as a subclass of contextfree languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptimecomplete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptimecomplete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined. 1
A Landscape with Games in the Background
 In 19th IEEE Symposium on Logic in Computer Science, LICS ’04
, 2004
"... An overview of applications of two player pathforming games to verification and synthesis is given. Several extensions of the standard model of finite games with regular winning conditions are discussed. One direction is that of considering nonregular winning conditions. The other concerns the w ..."
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An overview of applications of two player pathforming games to verification and synthesis is given. Several extensions of the standard model of finite games with regular winning conditions are discussed. One direction is that of considering nonregular winning conditions. The other concerns the ways games are played, in particular probabilistic and multiplayer games. 1
Games where you can play optimally without any memory
 In CONCUR 2005, LNCS
, 2005
"... Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently how ..."
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Abstract. Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or meanpayoff [5,6], previously used only in economic context, entered into the area of system modelling and verification. The most outstanding property of parity, meanpayoff and discounted games is the existence of optimal positional (memoryless) strategies for both players. This observation raises two questions: (1) can we characterise the family of payoff mappings for which there always exist optimal positional strategies for both players and (2) are there other payoff mappings with practical or theoretical interest and admitting optimal positional strategies. This paper provides a complete answer to the first question by presenting a simple necessary and sufficient condition on payoff mapping guaranteeing the existence of optimal positional strategies. As a corollary to this result we show the following remarkable property of payoff mappings: if both players have optimal positional strategies when playing solitary oneplayer games then also they have optimal positional strategies for twoplayer games.
Symbolic backwardsreachability analysis for higherorder pushdown systems
 IN FOSSACS
, 2007
"... Higherorder pushdown systems (PDSs) generalise pushdown systems through the use of higherorder stacks; that is, a nested “stack of stacks ” structure. These systems may be used to model higherorder programs and are closely related to the Caucal hierarchy of infinite graphs and safe higherorder ..."
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Cited by 16 (5 self)
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Higherorder pushdown systems (PDSs) generalise pushdown systems through the use of higherorder stacks; that is, a nested “stack of stacks ” structure. These systems may be used to model higherorder programs and are closely related to the Caucal hierarchy of infinite graphs and safe higherorder recursion schemes. We generalise higherorder PDSs to higherorder Alternating PDSs (APDSs) and consider the backwardsreachability problem over these systems. This builds on and extends previous work into pushdown systems and contextfree higherorder processes in a nontrivial manner. In particular, we show that the set of configurations from which a regular set of higherorder APDS configurations is reachable is regular and computable in nEXPTIME. In fact, the problem is nEXPTIMEcomplete. We show that this work has several applications in the verification of higherorder PDSs, such as lineartime modelchecking, alternationfree µcalculus modelchecking and the computation of winning regions of reachability games.
Halfpositional determinacy of infinite games
 In Proc. of ICALP’06, LNCS
, 2006
"... Abstract. We study infinite games where one of the players always has a positional (memoryless) winning strategy, while the other player may use a historydependent strategy. We investigate winning conditions which guarantee such a property for all arenas, or all finite arenas. We establish some cl ..."
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Abstract. We study infinite games where one of the players always has a positional (memoryless) winning strategy, while the other player may use a historydependent strategy. We investigate winning conditions which guarantee such a property for all arenas, or all finite arenas. We establish some closure properties of such conditions, and discover some common reasons behind several known and new positional determinacy results. We exhibit several new classes of winning conditions having this property: the class of concave conditions (for finite arenas) and the classes of monotonic conditions and geometrical conditions (for all arenas). 1
Degrees of Lookahead in Regular Infinite Games
"... Abstract. We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent ..."
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Abstract. We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent. This captures situations in distributed systems, e.g. when buffers are present in communication or when signal transmission between components is deferred. We distinguish strategies with different degrees of lookahead, among them being the continuous and the bounded lookahead strategies. In the first case the lookahead is of finite possibly unbounded size, whereas in the second case it is of bounded size. We show that for regular infinite games the solvability by continuous strategies is decidable, and that a continuous strategy can always be reduced to one of bounded lookahead. Moreover, this lookahead is at most doubly exponential in the size of the parity automaton recognizing the winning condition. We also show that the result fails for nonregular games where the winning condition is given by a contextfree ωlanguage. 1
Bounds in ωregularity
"... We consider an extension of ωregular expressions where two new variants of the Kleene star L ∗ are added: L B and L S. These exponents act as the standard star, but restrict the number of iterations to be bounded (for L B) or to tend toward infinity (for L S). These expressions can define languages ..."
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We consider an extension of ωregular expressions where two new variants of the Kleene star L ∗ are added: L B and L S. These exponents act as the standard star, but restrict the number of iterations to be bounded (for L B) or to tend toward infinity (for L S). These expressions can define languages that are not ωregular. We develop a theory for these languages. We study the decidability and closure questions. We also define an equivalent automaton model, extending Büchi automata. This culminates with a — partial — complementation result. 1