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The Owner Concept for PRAMs
, 1991
"... We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, ..."
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Cited by 17 (5 self)
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We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, it is shown that list ranking can be done in O(log n) time by an OROWPRAM and that LOGSPACE ` OROWTIME(log n). Then we prove that OROWPRAMs are a fairly robust model and recognize the same class of languages when the model is modified in several ways and that all kinds of PRAMs intertwine with the NC hierarchy without timeloss. Finally it is shown that EREWPRAMs can be simulated by OREWPRAMs and ERCWPRAMs by ORCWPRAMs. 3 This research was partially supported by the Deutsche Forschungsgemeinschaft, SFB 342, Teilprojekt A4 "Klassifikation und Parallelisierung durch Reduktionsanalyse" y Email: rossmani@lan.informatik.tumuenchen.dbp.de Introduction Fortune and Wyllie introduced in...
The complexity of membership problems for circuits over sets of natural numbers
, 2007
"... The problem of testing membership in the subset of the natural numbers produced at the output gate of a {∪, ∩, − , +, ×} combinational circuit is shown to capture a wide range of complexity classes. Although the general problem remains open, the case {∪, ∩, +, ×} is shown NEXPTIMEcomplete, the cas ..."
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Cited by 15 (0 self)
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The problem of testing membership in the subset of the natural numbers produced at the output gate of a {∪, ∩, − , +, ×} combinational circuit is shown to capture a wide range of complexity classes. Although the general problem remains open, the case {∪, ∩, +, ×} is shown NEXPTIMEcomplete, the cases {∪, ∩, − , ×}, {∪, ∩, ×}, {∪, ∩, +} are shown PSPACEcomplete, the case {∪, +} is shown NPcomplete, the case {∩, +} is shown C=Lcomplete, and several other cases are resolved. Interesting auxiliary problems are used, such as testing nonemptyness for unionintersectionconcatenation circuits, and expressing each integer, drawn from a set given as input, as powers of relatively prime integers of one’s choosing. Our results extend in nontrivial ways past work by
The Descriptive Complexity Approach to LOGCFL
, 1998
"... Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory ..."
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Cited by 12 (5 self)
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Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the contextfree languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFLcomplete under quantifierfree BITfree projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that firstorder logic with majority of pairs is strictly more expressive than firstorder with major...
On Growing ContextSensitive Languages
 Proc. 19th ICALP, Lecture Notes in Computer Science (W. Kuich,ed
, 1992
"... Growing contextsensitive grammars (GCSG) are investigated. The variable membership problem for GCSG is shown to be NPcomplete. This solves a problem posed in [DW86]. It is also shown that the languages generated by GCSG form an abstract family of languages and several implications are presented. ..."
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Cited by 11 (2 self)
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Growing contextsensitive grammars (GCSG) are investigated. The variable membership problem for GCSG is shown to be NPcomplete. This solves a problem posed in [DW86]. It is also shown that the languages generated by GCSG form an abstract family of languages and several implications are presented. Institut fur Informatik, Universitat Wurzburg, D8700 Wurzburg, Germany. y Instytut Informatyki, Uniwersytet Wroc/lawski, 51151 Wroc/law, Poland (permanent address). This research was supported by the Humboldt Foundation. 1 Introduction It is well known that the class of languages generated by contextsensitive grammars is equal to NSPACE(n) and that, even for fixed grammars, the membership problem can be PSPACEcomplete. On the other hand the contextfree grammars are known to have, for many applications, too weak derivative power. While many modifications extending contextfree grammars have been studied, only a few papers concern some restricted versions of contextsensitive gramm...
Evaluating monotone circuits on cylinders, planes, and tori
 IN PROC. 23RD SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTING (STACS), LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strictly gener ..."
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We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strictly generalizes upward planarity, and make the characterization partially constructive. We use this construction, and four key reduction lemmas, to obtain several improvements. We show that monotone circuits with embeddings that are stratified cylindrical, cylindrical, planar oneinputface and focused can be evaluated in LogDCFL, AC 1 (LogDCFL), LogCFL and AC 1 (LogDCFL) respectively. We note that the NC 3 algorithm for general MPCVP is in AC 1 (LogCFL) =SAC 2.Finally, we show that monotone circuits with toroidal embeddings can, given such an embedding, be evaluated in NC.
The Complexity of Computing over Quasigroups
, 1994
"... In [7] the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. This led to a new characterization of the contextfree languages and the class SAC¹. In this paper, we investigate the classes of languages obtained when the groupoids are restricted to be ..."
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Cited by 11 (6 self)
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In [7] the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. This led to a new characterization of the contextfree languages and the class SAC¹. In this paper, we investigate the classes of languages obtained when the groupoids are restricted to be quasigroups (i.e. the multiplication table forms a latin square). We prove that languages recognized by quasigroups are regular and that programs over quasigroups characterize NC¹. We introduce the notions of linear recognition by groupoids and by programs over groupoids, and characterize the linear contextfree languages and NL. Here again, when quasigroups are used, only regular languages and languages in NC¹ can be obtained. We also consider the problem of evaluating a wellparenthesized expression over a finite loop (a quasigroup with an identity). This problem is in NC¹ for any finite loop, and we give algebraic conditions for its completeness. In particular, we prove that it is sufficient that the loop be nonsolvable, extending a wellknown theorem of Barrington ([3]).
Advocating Ownership
, 1996
"... . We show the equivalence of deterministic auxiliary pushdown automata to owner write PRAMs in a fairly large setting by proving that DAuxPDATISP \Gamma f O(1) ; log g \Delta and CROWTIPR \Gamma log f; g O(1) \Delta coincide. Such, we provide the first circuit characterizations of depth ..."
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Cited by 10 (5 self)
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. We show the equivalence of deterministic auxiliary pushdown automata to owner write PRAMs in a fairly large setting by proving that DAuxPDATISP \Gamma f O(1) ; log g \Delta and CROWTIPR \Gamma log f; g O(1) \Delta coincide. Such, we provide the first circuit characterizations of depth O(log f) for deterministic sequential automata which are f timebounded. 1 Introduction Parallel models provided fruitful extensions to structural complexity theory, a prominent example being the class NC . Ruzzo exhibited the tight connections between alternating Turing machines, auxiliary pushdown automata, and boolean circuits [20]. By results of Stockmeyer and Vishkyn [21] and by the intertwining of the NC hierarchy with the polylogtime hierarchy of EREWPRAMs these relations are also valid for the various types of PRAMs defined by the concurrent and the exclusive read and write feature. In 1986, Dymond and Ruzzo introduced the concept of owner write for PRAMs and showed close conn...
Characterizing Unambiguous Augmented Pushdown Automata by Circuits
 In Proc. of 15th Symposium on Mathematical Foundations of Computer Science, number 452 in LNCS
, 1990
"... The notions of weak and strong unambiguity of augmented pushdown automata are considered and related to unambiguities of circuits. In particular we exhibit circuit classes exactly characterizing polynomially time bounded unambiguous augmented pushdown automata. Introduction An important objec ..."
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The notions of weak and strong unambiguity of augmented pushdown automata are considered and related to unambiguities of circuits. In particular we exhibit circuit classes exactly characterizing polynomially time bounded unambiguous augmented pushdown automata. Introduction An important object in parallel complexity theory, the class NC , can be characterized in terms of Parallel Random Access Machines, see e.g. [3, 4, 9], Boolean Circuits [3, 10], Augmented Pushdown Automata [7, 6], and Alternating Turing Machines [1, 7]. There are close connections between these concepts, see e.g. [3, 5]. In [5] unambiguous circuits were considered in order to characterize CREWPRAMs and to further relate them with the NC structure. Working with unambiguity we must distinguish between the notions of unambiguity and uniqueness. While uniqueness uses the unique existence of a computation path as a tool for acceptance, unambiguity requires this unique existence for all accepting computation pat...
Arithmetic Complexity, Kleene Closure, and Formal Power Series
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 8 (1999)
, 1999
"... The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC 1 and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity ..."
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Cited by 7 (3 self)
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The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC 1 and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity classes. We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC 1 and GapL. We prove that Kleene closure, inversion, and root extraction are all hard operations in the following sense: There is a language in AC 0 for which inversion and root extraction are GapLcomplete, and there is a finite set for which inversion and root extraction are GapNC 1complete, with respect to appropriate reducibilities. The latter result raises the question of classifying finite languages so that their inverses fall within interesting subclasses of GapNC 1, such as GapAC 0. We initiate work in this direction by classifying the complexity of the Kleene closure of finite languages. We formulate the problem in terms of finite monoids and relate its complexity to the internal structure of the monoid.