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ContextFree Languages and PushDown Automata
 Handbook of Formal Languages
, 1997
"... Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : ..."
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Cited by 72 (0 self)
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Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2. Systems of equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.1 Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Resolution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.3 Linear systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.4 Parikh's theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
The Computational Analysis of the Syntax and Interpretation of "Free" Word Order in Turkish
, 1995
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The computational power of population protocols
 Distributed Computing
"... We consider the model of population protocols introduced by Angluin et al. [AAD + 04], in which anonymous finitestate agents stably compute a predicate of the multiset of their inputs via twoway interactions in the allpairs family of communication networks. We prove that all predicates stably com ..."
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Cited by 61 (4 self)
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We consider the model of population protocols introduced by Angluin et al. [AAD + 04], in which anonymous finitestate agents stably compute a predicate of the multiset of their inputs via twoway interactions in the allpairs family of communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of twoway interaction, we also consider several variants of the model in which agents communicate by anonymous messagepassing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These oneway models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these oneway models using natural subclasses of the semilinear predicates. 1
Counting in Trees for Free
, 2004
"... In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logi ..."
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Cited by 48 (2 self)
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In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logic by means of deterministic Presburger tree automata (PTA) and show how it can be used to express numerical document queries. Surprisingly, the complexity of satisfiability for the extended logic is asymptotically the same as for the original logic. The nonemptiness for PTAs is in general pspacecomplete which is moderate given that it is already pspacehard to test whether the complement of a regular expression is nonempty. We also identify a subclass of PTAs with a tractable nonemptiness problem. Further, to decide whether a tree t satisfies a formula # is polynomial in the size of # and linear in the size of t.
A robust class of contextsensitive languages
 In LICS
, 2007
"... We define a new class of languages defined by multistack automata that forms a robust subclass of contextsensitive languages, with decidable emptiness and closure under boolean operations. This class, called multistack visibly pushdown languages (MVPLs), is defined using multistack pushdown auto ..."
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We define a new class of languages defined by multistack automata that forms a robust subclass of contextsensitive languages, with decidable emptiness and closure under boolean operations. This class, called multistack visibly pushdown languages (MVPLs), is defined using multistack pushdown automata with two restrictions: (a) the pushdown automaton is visible, i.e. the input letter determines the operation on the stacks, and (b) any computation of the machine can be split into�stages, where in each stage, there is at most one stack that is popped. MVPLs are an extension of visibly pushdown languages that captures noncontext free behaviors, and has applications in analyzing abstractions of multithreaded recursive programs, significantly enlarging the search space that can be explored for them. We show that MVPLs are closed under boolean operations, and problems such as emptiness and inclusion are decidable. We characterize MVPLs using monadic secondorder logic over appropriate structures, and exhibit a Parikh theorem for them. 1.
Interprocedural Analysis of Asynchronous Programs
, 2007
"... An asynchronous program is one that contains procedure calls which are not immediately executed from the callsite, but stored and “dispatched” in a nondeterministic order by an external scheduler at a later point. We formalize the problem of interprocedural dataflow analysis for asynchronous progra ..."
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Cited by 38 (5 self)
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An asynchronous program is one that contains procedure calls which are not immediately executed from the callsite, but stored and “dispatched” in a nondeterministic order by an external scheduler at a later point. We formalize the problem of interprocedural dataflow analysis for asynchronous programs as AIFDS problems, a generalization of the IFDS problems for interprocedural dataflow analysis. We give an algorithm for computing the precise meetovervalidpaths solution for any AIFDS instance, as well as a demanddriven algorithm for solving the corresponding demand AIFDS instances. Our algorithm can be easily implemented on top of any existing interprocedural dataflow analysis framework. We have implemented the algorithm on top of BLAST, thereby obtaining the first safety verification tool for unbounded asynchronous programs. Though the problem of solving AIFDS instances is EXPSPACEhard, we find that in practice our technique can efficiently analyze programs by exploiting standard optimizations of interprocedural dataflow analyses.
Model checking multithreaded programs with asynchronous atomic methods
 In CAV 06, LNCS 4314
, 2006
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Semilinearity as a Syntactic Invariant
, 1996
"... . Mildly context sensitive grammar formalisms such as multicomponent TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a nonsemilinear languag ..."
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Cited by 30 (9 self)
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. Mildly context sensitive grammar formalisms such as multicomponent TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a nonsemilinear language. This implies that none of the aforementioned grammar formalisms is strong enough to generate this language. Introduction What we have in mind when we use the term syntactic invariant is, roughly speaking, a property, valid within some (formal) grammar theory, which remains "robust under slight modifications" of this theory. In the following we direct our particular attention to one such property: Semilinearity (of a language). Introducing the definition of semilinearity Parikh proved that any context free language (CFL) is semilinear (see e.g. Parikh 1966). It has been shown that there is a need to go beyond the class of all CFLs, if we want to define a formal language in terms of phr...
Complexity of TwoDimensional Patterns
, 2000
"... In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are wellestablished classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of se ..."
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Cited by 26 (4 self)
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In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are wellestablished classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for twoormoredimensional patterns. We show that several de nitions of "regular language" or "local rule" that are equivalent in d = 1 lead to distinct classes in d 2. We explore the closure properties and computational complexity of these classes, including undecidability and L, NL and NPcompleteness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finitetime images, and limit sets. We show that it is undecidable whether a CA in d 2 has a periodic point of a given peri...
The Tree Width of Auxiliary Storage
"... 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 finitestate grap ..."
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Cited by 24 (2 self)
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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 finitestate graph automata (without storage) restricted to monadic secondorder (MSO) definable graphs of bounded treewidth, 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. Categories and Subject Descriptors F.1.1 [Theory of Computation]: