Showing papers on "Pushdown automaton published in 2003"
15 Dec 2003
TL;DR: Two equivalent characterizations of the Caucal hierarchy are given, one of which replaces the language-theoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation and the second is non-iterative.
Abstract: In this paper we give two equivalent characterizations of the Caucal hierarchy, a hierarchy of infinite graphs with a decidable monadic second-order (MSO) theory. It is obtained by iterating the graph transformations of unfolding and inverse rational mapping. The first characterization sticks to this hierarchical approach, replacing the language-theoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation. The second characterization is non-iterative. We show that the family of graphs of the Caucal hierarchy coincides with the family of graphs obtained as the e-closure of configuration graphs of higher-order pushdown automata.
114 citations
01 Jan 2003
TL;DR: Questions on RNA Secondary Structure Prediction and Design, Some Issues Regarding Search, Censorship, and Anonymity in Peer to Peer Networks, and Model Checking and Testing Combined.
Abstract: Invited Lectures.- Polarized Process Algebra and Program Equivalence.- Problems on RNA Secondary Structure Prediction and Design.- Some Issues Regarding Search, Censorship, and Anonymity in Peer to Peer Networks.- The SPQR-Tree Data Structure in Graph Drawing.- Model Checking and Testing Combined.- Logic and Automata: A Match Made in Heaven.- Algorithms.- Pushdown Automata and Multicounter Machines, a Comparison of Computation Modes.- Generalized Framework for Selectors with Applications in Optimal Group Testing.- Decoding of Interleaved Reed Solomon Codes over Noisy Data.- Process Algebra.- On the Axiomatizability of Ready Traces, Ready Simulation, and Failure Traces.- Resource Access and Mobility Control with Dynamic Privileges Acquisition.- Replication vs. Recursive Definitions in Channel Based Calculi.- Approximation Algorithms.- Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem.- An Improved Approximation Algorithm for the Asymmetric TSP with Strengthened Triangle Inequality.- An Improved Approximation Algorithm for Vertex Cover with Hard Capacities.- Approximation Schemes for Degree-Restricted MST and Red-Blue Separation Problem.- Approximating Steiner k-Cuts.- MAX k-CUT and Approximating the Chromatic Number of Random Graphs.- Approximation Algorithm for Directed Telephone Multicast Problem.- Languages and Programming.- Mixin Modules and Computational Effects.- Decision Problems for Language Equations with Boolean Operations.- Generalized Rewrite Theories.- Complexity.- Sophistication Revisited.- Scaled Dimension and Nonuniform Complexity.- Quantum Search on Bounded-Error Inputs.- A Direct Sum Theorem in Communication Complexity via Message Compression.- Data Structures.- Optimal Cache-Oblivious Implicit Dictionaries.- The Cell Probe Complexity of Succinct Data Structures.- Succinct Representations of Permutations.- Succinct Dynamic Dictionaries and Trees.- Graph Algorithms.- Labeling Schemes for Weighted Dynamic Trees.- A Simple Linear Time Algorithm for Computing a (2k - 1)-Spanner of O(n 1+1/k ) Size in Weighted Graphs.- Multicommodity Flows over Time: Efficient Algorithms and Complexity.- Multicommodity Demand Flow in a Tree.- Automata.- Skew and Infinitary Formal Power Series.- Nondeterminism versus Determinism for Two-Way Finite Automata: Generalizations of Sipser's Separation.- Residual Languages and Probabilistic Automata.- A Testing Scenario for Probabilistic Automata.- The Equivalence Problem for t-Turn DPDA Is Co-NP.- Flip-Pushdown Automata: k + 1 Pushdown Reversals Are Better than k.- Optimization and Games.- Convergence Time to Nash Equilibria.- Nashification and the Coordination Ratio for a Selfish Routing Game.- Stable Marriages with Multiple Partners: Efficient Search for an Optimal Solution.- An Intersection Inequality for Discrete Distributions and Related Generation Problems.- Graphs and Bisimulation.- Higher Order Pushdown Automata, the Caucal Hierarchy of Graphs and Parity Games.- Undecidability of Weak Bisimulation Equivalence for 1-Counter Processes.- Bisimulation Proof Methods for Mobile Ambients.- On Equivalent Representations of Infinite Structures.- Online Problems.- Adaptive Raising Strategies Optimizing Relative Efficiency.- A Competitive Algorithm for the General 2-Server Problem.- On the Competitive Ratio for Online Facility Location.- A Study of Integrated Document and Connection Caching.- Verification.- A Solvable Class of Quadratic Diophantine Equations with Applications to Verification of Infinite-State Systems.- Monadic Second-Order Logics with Cardinalities.- ? 2 ? ? 2 ? AFMC.- Upper Bounds for a Theory of Queues.- Around the Internet.- Degree Distribution of the FKP Network Model.- Similarity Matrices for Pairs of Graphs.- Algorithmic Aspects of Bandwidth Trading.- Temporal Logic and Model Checking.- CTL+ Is Complete for Double Exponential Time.- Hierarchical and Recursive State Machines with Context-Dependent Properties.- Oracle Circuits for Branching-Time Model Checking.- Graph Problems.- There Are Spanning Spiders in Dense Graphs (and We Know How to Find Them).- The Computational Complexity of the Role Assignment Problem.- Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs.- Genus Characterizes the Complexity of Graph Problems: Some Tight Results.- Logic and Lambda-Calculus.- The Definition of a Temporal Clock Operator.- Minimal Classical Logic and Control Operators.- Counterexample-Guided Control.- Axiomatic Criteria for Quotients and Subobjects for Higher-Order Data Types.- Data Structures and Algorithms.- Efficient Pebbling for List Traversal Synopses.- Function Matching: Algorithms, Applications, and a Lower Bound.- Simple Linear Work Suffix Array Construction.- Types and Categories.- Expansion Postponement via Cut Elimination in Sequent Calculi for Pure Type Systems.- Secrecy in Untrusted Networks.- Locally Commutative Categories.- Probabilistic Systems.- Semi-pullbacks and Bisimulations in Categories of Stochastic Relations.- Quantitative Analysis of Probabilistic Lossy Channel Systems.- Discounting the Future in Systems Theory.- Information Flow in Concurrent Games.- Sampling and Randomness.- Impact of Local Topological Information on Random Walks on Finite Graphs.- Analysis of a Simple Evolutionary Algorithm for Minimization in Euclidean Spaces.- Optimal Coding and Sampling of Triangulations.- Generating Labeled Planar Graphs Uniformly at Random.- Scheduling.- Online Load Balancing Made Simple: Greedy Strikes Back.- Real-Time Scheduling with a Budget.- Improved Approximation Algorithms for Minimum-Space Advertisement Scheduling.- Anycasting in Adversarial Systems: Routing and Admission Control.- Geometric Problems.- Dynamic Algorithms for Approximating Interdistances.- Solving the Robots Gathering Problem.
105 citations
Book•
01 Jan 2003
TL;DR: A Cryptographically Sound Security Proof of the Needham-Schroeder-Lowe Public-Key Protocol and Analysis and Experimental Evaluation of a Simple Algorithm for Collaborative Filtering in Planted Partition Models.
Abstract: Contributed Papers.- A Cryptographically Sound Security Proof of the Needham-Schroeder-Lowe Public-Key Protocol.- Constructions of Sparse Asymmetric Connectors.- A Separation Logic for Resource Distribution.- An Equational Theory for Transactions.- Axioms for Regular Words.- 1-Bounded TWA Cannot Be Determinized.- Reachability Analysis of Process Rewrite Systems.- Pushdown Games with Unboundedness and Regular Conditions.- Real-Time Model-Checking: Parameters Everywhere.- The Caucal Hierarchy of Infinite Graphs in Terms of Logic and Higher-Order Pushdown Automata.- Deciding the Security of Protocols with Diffie-Hellman Exponentiation and Products in Exponents.- Subtyping Constraints in Quasi-lattices.- An Improved Approximation Scheme for Computing Arrow-Debreu Prices for the Linear Case.- Word Equations over Graph Products.- Analysis and Experimental Evaluation of a Simple Algorithm for Collaborative Filtering in Planted Partition Models.- Comparing Sequences with Segment Rearrangements.- On Logically Defined Recognizable Tree Languages.- Randomized Time-Space Tradeoffs for Directed Graph Connectivity.- Distance-Preserving Approximations of Polygonal Paths.- Joint Separation of Geometric Clusters and the Extreme Irregularities of Regular Polyhedra.- On the Covering Steiner Problem.- Minimality Results for the Spatial Logics.- Algorithms for Non-uniform Size Data Placement on Parallel Disks.- Efficient Algorithms for Abelian Group Isomorphism and Related Problems.- Quasi-polynomial Time Approximation Algorithm for Low-Degree Minimum-Cost Steiner Trees.- Model Checking and Satisfiability for Sabotage Modal Logic.- Merging and Sorting By Strip Moves.- The Macro Tree Transducer Hierarchy Collapses for Functions of Linear Size Increase.- Distributed Games.- Maintenance of Multidimensional Histograms.- Tagging Makes Secrecy Decidable with Unbounded Nonces as Well.- Quantum and Classical Complexity Classes: Separations, Collapses, and Closure Properties.- On the Greedy Superstring Conjecture.- Invited Papers.- Reasoning about Infinite State Systems Using Boolean Methods.- Stringent Relativization.- Component-Based Construction of Deadlock-Free Systems.- Moderately Hard Functions: From Complexity to Spam Fighting.- Zigzag Products, Expander Constructions, Connections, and Applications.
105 citations
TL;DR: Summarily formal aspect of CW is more systematically established more deeply dealt with while some new problems also emerge.
Abstract: Computing with words (CW) as a methodology, means computing and reasoning by the use of words in place of numbers or symbols, which may conform more to humans' perception when describing real-world problems. In this paper, as a continuation of a previous paper, we aim to develop and deepen a formal aspect of CW. According to the previous paper, the basic point of departure is that CW treats certain formal modes of computation with strings of fuzzy subsets instead of symbols as their inputs. Specifically, 1) we elaborate on CW via Turing machine (TM) models, showing the time complexity is at least exponential if the inputs are strings of words; 2) a negative result of (6) not holding is verified which indicates that the extension principle for CW via TMs needs to be re-examined; 3) we discuss CW via context- free grammars and regular grammars and the extension principles for CW via these formal grammars are set up; 4) some equivalences between fuzzy pushdown automata (respectively, fuzzy finite-state automata) fuzzy context-free grammars (respectively, fuzzy regular grammars) are demonstrated in the sense that the inputs are instead strings of words; 5) some instances are described in detail. Summarily formal aspect of CW is more systematically established more deeply dealt with while some new problems also emerge.
70 citations
30 Jun 2003
TL;DR: This work considers two-player parity games played on transition graphs of higher order pushdown automata and shows how to reduce a game to a graph of lower level, leading to an effective solution and a construction of the winning strategies.
Abstract: We consider two-player parity games played on transition graphs of higher order pushdown automata. They are "game-equivalent" to a kind of model-checking game played on graphs of the infinite hierarchy introduced recently by Caucal. Then in this hierarchy we show how to reduce a game to a graph of lower level. This leads to an effective solution and a construction of the winning strategies.
68 citations
TL;DR: Since a timed automaton can be treated as a PTA without the pushdown stack, it can be shown that the binary reachability of a timedAutomaton is definable in the additive theory of reals and integers.
59 citations
28 Jun 2003
TL;DR: It is shown that a tree language recognizing by a deterministic parity automaton is either hard for the co-Buchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy ofWeak alternating automata.
Abstract: We show that a tree language recognized by a deterministic parity automaton is either hard for the co-Buchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. A topological counterpart of this property is that a deterministic tree language is either Π11 complete (and hence nonBorel), or it is on the level Π30 of the Borel hierarchy. We also give a new simple proof of the strictness of the hierarchy of weak alternating automata.
59 citations
15 Dec 2003
TL;DR: It is shown that the problem of deciding a winner in infinitary two-player perfect information games defined over graphs of configurations of a pushdown automaton is EXPTIME-complete.
Abstract: We consider infinitary two-player perfect information games defined over graphs of configurations of a pushdown automaton We show how to solve such games when winning conditions are Boolean combinations of a Buchi condition and a new condition that we call unboundedness An infinite play satisfies the unboundedness condition if there is no bound on the size of the stack during the play We show that the problem of deciding a winner in such games is EXPTIME-complete
50 citations
TL;DR: The Wadge hierarchy of context-free ?
46 citations
30 Jun 2003
TL;DR: It is shown that k+1 pushdown reversals are better than k for both deterministic and nondeterministic flip-pushdown automata, and closure and non-closure properties as well as computational complexity problems such as fixed and general membership are investigated.
Abstract: Flip-pushdown automata are pushdown automata with the additional power to flip or reverse its pushdown, and were recently introduced by Sarkar [13]. We solve most of Sarkar's open problems. In particular, we show that k+1 pushdown reversals are better than k for both deterministic and nondeterministic flip-pushdown automata, i.e., there are languages which can be recognized by a deterministic flip-pushdown automaton with k+1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic). Furthermore, we investigate closure and non-closure properties as well as computational complexity problems such as fixed and general membership.
37 citations
Dissertation•
01 Jan 2003
TL;DR: This work considers several classes of infinite graphs, from transition graphs of pushdown automata up to graphs of the Caucal hierarchy, and investigates different winning conditions: reachability, recurrence, parity, and the a called Σ3-condition.
Abstract: Two player games are a standard model of reactive computation, where e.g. one player is the controller and the other is the environment. A game is won by a player if she has a winning strategy, i.e., if she can win every play. Given a finite description of the game, our aim is to compute the winner and a winning strategy. For finite graphs these problems have been solved for a long time, although some complexity questions remain open. We consider several classes of infinite graphs, from transition graphs of pushdown automata up to graphs of the Caucal hierarchy, and we investigate different winning conditions: reachability, recurrence (Büchi), parity, and the a called Σ3-condition. Two kinds of techniques are developed: a symbolic approach based on finite automata recognizing infinite sets of configurations and a game simulation which reduces a given game into a simpler one and solves it. Different kinds of strategies are also constructed: either positional or based on pushdown stack memories.
08 Dec 2003
TL;DR: An extension of the learning classifier system XCS is presented in which classifier conditions are represented by RPN expressions and stack-based genetic programming is used to recombine and mutate classifiers.
Abstract: We present an extension of the learning classifier system XCS in which classifier conditions are represented by RPN expressions and stack-based genetic programming is used to recombine and mutate classifiers. In contrast with other extensions of XCS involving tree-based genetic programming, the representation we apply here produces conditions that are linear programs, interpreted by a virtual stack machine (similar to a pushdown automaton), and recombined through standard genetic operators. We test the version of XCS extended with stack-based conditions on a set of problems of different complexity.
TL;DR: It is proved that non Borel omega context free languages which are recognized by Buchi pushdown automata have a maximum degree of ambiguity, which implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language.
Abstract: We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free languages which are recognized by Buchi pushdown automata have a maximum degree of ambiguity. This result implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language. We prove also that taking the adherence or the delta-limit of a finitary language preserves neither unambiguity nor inherent ambiguity. On the other side we show that methods used in the study of omega context free languages can also be applied to study the notion of ambiguity in infinitary rational relations accepted by Buchi 2-tape automata and we get first results in that direction.
Journal Article•
TL;DR: In this article, the authors investigated deterministic and non-deterministic flip-pushdown automata accepting by final state or empty pushdown and showed that nondeterminism is better than determinism.
Abstract: Flip-pushdown automata are pushdown automata with the additional ability to flip or reverse its pushdown. We investigate deterministic and nondeterministic flip-pushdown automata accepting by final state or empty pushdown. In particular, for nondeterministic flip-pushdown automata both acceptance criterion are equally powerful, while for determinism, acceptance by empty pushdown is strictly weaker. This nicely fits into the well-known results on ordinary pushdown automata. Moreover, we consider hierarchies of flip-pushdown automata w.r.t. the number of pushdown reversals. There we show that nondeterminism is better than determinism. Moreover, since there are languages which can be recognized by a deterministic flip-pushdown automaton with k + 1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic) as shown in [9] we are able to complete our investigations with incomparabiiity results on different levels of the hierarchies under consideration.
TL;DR: It is shown that the notions of ambiguity and of degrees of ambiguity of finitary context free languages may be defined independently of the Buchi or Muller acceptance condition which is considered.
07 Jul 2003
TL;DR: Deterministic and nondeterministic flip-pushdown automata accepting by final state or empty pushdown are investigated and it is shown that nondeterminism is better than determinism.
Abstract: Flip-pushdown automata are pushdown automata with the additional ability to flip or reverse its pushdown We investigate deterministic and nondeterministic flip-pushdown automata accepting by final state or empty pushdown In particular, for nondeterministic flip-pushdown automata both acceptance criterion are equally powerful, while for determinism, acceptance by empty pushdown is strictly weaker This nicely fits into the well-known results on ordinary pushdown automata Moreover, we consider hierarchies of flip-pushdown automata wrt the number of pushdown reversals There we show that nondeterminism is better than determinism Moreover, since there are languages which can be recognized by a deterministic flip-pushdown automaton with k + 1 pushdown reversals but which cannot be recognized by a k-flip-pushdown (deterministic or nondeterministic) as shown in [9] we are able to complete our investigations with incomparability results on different levels of the hierarchies under consideration
Journal Article•
TL;DR: A fundamental framework of automata and grammars theory based on quantum logic is preliminarily established and it is showed that the language generated by any l valued regular grammar is equivalent to that recognized by some automaton with e moves based onquantum logic.
Abstract: In this paper, a fundamental framework of automata and grammars theory based on quantum logic is preliminarily established. First, the introduce quantum grammar, which is called l valued grammars, is introduced. It is particularly showed that the language (called quantum language) generated by any l valued regular grammar is equivalent to that recognized by some automaton with e moves based on quantum logic (called l valued automata), and conversely, any quantum language recognized by l valued automaton is also equivalent to that generated by some l valued grammar. Afterwards, the l valued pumping lemma is built, and then a decision characterization of quantum languages is presented. Finally, the relationship between regular grammars and quantum grammars (l valued regular grammars) is briefly discussed. Summarily, the introduced work lays a foundation for further studies on more complicated quantum automata and quantum grammars such as quantum pushdown automata and Turing machine as well as quantum context-free grammars and context-sensitive grammars.
Posted Content•
TL;DR: In this paper, it was shown that an f(p)-coin can be simulated by a pushdown automata if and only if f is a rational function over Q. The results of this paper are also related to the results of O'Brien et al. who showed that pushdown-automata can be used to simulate non-rational functions such as the square root of p.
Abstract: Suppose that we are given a function f : (0,1) -> (0,1) and, for some unknown p in (0,1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of ``heads'').
For which functions f is it possible to simulate an f(p)-coin?; This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function 1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)-coin can be simulated by a finite automaton for all p in (0,1), if and only if f is a rational function over Q. We also show that if an f(p)-coin can be simulated by a pushdown automaton, then f is an algebraic function over Q; however, pushdown automata can simulate f(p)-coins for certain non-rational functions such as the square root of p. These results complement the work of Keane and O'Brien (1994), who determined the functions $f$ for which an f(p)-coin can be simulated when there are no computational restrictions on the simulation scheme.
01 Jan 2003
TL;DR: In this paper, the authors investigated the descriptional complexity of deterministic two-way k-head finite automata (k- DHA) and showed that for any k-DHA, k ≥ 2, there are savings in the size of description which cannot be bounded by any recursive function.
Abstract: We investigate the descriptional complexity of deterministic two-way k-head finite automata (k- DHA). It is shown that between non-deterministic pushdown automata and any k-DHA, k ≥ 2, there are savings in the size of description which cannot be bounded by any recursive function. The same is true for the other end of the hierarchy. Such non-recursive trade-offs are also shown between any k-DHA, k ≥ 1, and DSPACE(log) = multi-DHA. We also address the particular case of unary languages. In general, it is possible that non-recursive trade-offs for arbitrary languages reduce to recursive trade-offs for unary languages. Here we present huge lower bounds for the unary trade-offs between non-deterministic finite automata and any k-DHA, k ≥ 2. Furthermore, several known simulation results imply the presented trade-offs for other descriptional systems, e.g., deterministic two-way finite automata with k pebbles or with k linearly bounded counters.
07 Jul 2003
TL;DR: In this article, the relationship between the minimal automaton, the universal automaton and the syntactic monoid of a regular language is discussed, and certain completions and reductions of the transformation matrix of the automaton are discussed.
Abstract: We discuss the relationships between the minimal automaton, the universal automaton, the syntactic monoid and the syntactic semiring of a given regular language We use certain completions and reductions of the transformation matrix of the minimal automaton to clarify those connections
Journal Article•
TL;DR: Certain completions and reductions of the transformation matrix of the minimal automaton are used to clarify connections between the relationships between the minimal Automaton, the universal automaton,The syntactic monoid and the syntactic semiring of a given regular language.
Abstract: We discuss the relationships between the minimal automaton, the universal automaton, the syntactic monoid and the syntactic semiring of a given regular language. We use certain completions and reductions of the transformation matrix of the minimal automaton to clarify those connections.
26 Jun 2003
TL;DR: This text sketches a method based on adaptive technology for representing context-dependencies in NL processing that relies on adaptive structured pushdown automata and grammars for simplicity, low-cost and efficiency.
Abstract: This text sketches a method based on adaptive technology for representing context-dependencies in NL processing. Based on a previous work [4] dedicated to syntactical ambiguities and nondeterminisms in NL handling we extend it to consider context-dependencies not previously addressed. Although based on the powerful adaptive formalism [3], our method relies on adaptive structured pushdown automata [1] and grammars [2] - resulting simplicity, low-cost and efficiency.
TL;DR: A study on how students perceived non-determinism of finite automata in a theoretical unit on computational models found that many students did not choose the easiest way to solve the problem: Many students preferred to construct a deterministic automaton, even though constructing a non-Determinism automaton for the language is much simpler.
Abstract: One of the units in the relatively new high school CS curriculum which is being implemented in Israel is a theoretical unit on computational models. It includes deterministic and non-deterministic finite automata, regular and non-regular languages, closure properties of regular languages, pushdown automata, closure properties of context free languages, turing machines, the church-turing thesis and the halting problem. This paper focuses on part of a study we conducted on the unit, dealing with the topic of non-determinism of finite automata. One of the aspects dealt with was how students perceived non-determinism. 339 students were given a relatively complicated regular language, and asked to construct a finite automaton that accepts this language. We found that many students did not choose the easiest way to solve the problem: Many students preferred to construct a deterministic automaton, even though constructing a non-deterministic automaton for the language is much simpler. We analyze and categorize the students' solutions, thus shedding some light on their perception of the abstract concept of non-determinism.
16 Jul 2003
TL;DR: It is shown that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language.
Abstract: Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.
Journal Article•
TL;DR: This work introduces distributed pushdown automata systems consisting of several push down automata which work in turn on the input string placed on a common one-way input tape, and investigates the computational power of these mechanisms under different protocols for activating components and two ways of accepting the inputstring.
Abstract: We introduce distributed pushdown automata systems consisting of several pushdown automata which work in turn on the input string placed on a common one-way input tape. The work of the components is based on protocols and strategies similar to those that cooperating distributed grammar systems use. We investigate the computational power of these mechanisms under different protocols for activating components and two ways of accepting the input string: with empty stacks or with final states which means that all components have empty stacks or are in final states, respectively, when the input string was completely read.
30 Jun 2003
TL;DR: Here, the polynomial-time classes of multicounter machines with a constant number of reversals are considered and the computational power of nondeterminism, randomization and determinism is separated.
Abstract: There are non-context-free languages which are recognizable by randomized pushdown automata even with arbitrarily small error probability. We give an example of a context-free language which cannot be recognized by a randomized pda with error probability smaller than 1/2 - O(log2 n/n) for input size n. Hence nondeterminism can be stronger than probabilism with weakly-unbounded error.
Moreover, we construct two deterministic context-free languages whose union cannot be accepted with error probability smaller than 1/3-2-Ω(n), where n is the input length. Since the union of any two deterministic context-free languages can be accepted with error probability 1/3, this shows that 1/3 is a sharp threshold and hence randomized pushdown automata do not have amplification.
One-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism.
Journal Article•
TL;DR: It is proved that all these systems accept the family of recursively enumerable languages both in the centralized and in the non-centralized strategies and in both returning and non-returning communication modes with only two components.
Abstract: We consider automata systems consisting of several pushdown automata working in parallel and communicating the contents of their stacks by request. We show that centralized non-returning parallel communicating pushdown automata systems with three components recognize all recursively enumerable languages. We also show that centralized returning pushdown automata systems accept non-ET0L languages. We study two variants of communication: one uses filters in communication and in the other only specified number of symbols are communicated. We prove that all these systems accept the family of recursively enumerable languages both in the centralized and in the non-centralized strategies and in both returning and non-returning communication modes with only two components.
16 Jul 2003
TL;DR: The notion of a well-formed bag automaton, which is used to model the inherent problems associated with the retrieval of biomolecules from solution, is defined.
Abstract: In this paper, we define the notion of a well-formed bag automaton, which is used to model the inherent problems associated with the retrieval of biomolecules from solution.We will consider the computational power and other properties of non-deterministic and deterministic, well-formed bag automata.
TL;DR: This paper gives a counterexample to the original KC-DCF lemma and also provides a corrected version, which works on a superset of examples compared to traditional iteration and pumping lemmas.
Abstract: We deal with a criterion for deterministic context-free languages that was originally formulated by Li and Vitanyi [SIAM J. Comput., 24 (1995), pp. 398--410]. Their result---called the KC-DCF lemma---relates Kolmogorov complexity to pushdown automata and works on a superset of examples compared to traditional iteration and pumping lemmas. Sadly, their KC-DCF lemma has a flaw. In this paper, we give a counterexample to the original KC-DCF lemma and also provide a corrected version.
Journal Article•
TL;DR: It is proved that the size of the subsequence automaton for a set of k strings of length n is Ω(n k ) for any k≥ 1, which solves an open problem posed by Crochemore and Tronicek in 1999.
Abstract: Given a set of strings, the subsequence automaton accepts all subsequences of these strings. We will derive a lower bound for the maximum number of states of this automaton. We will prove that the size of the subsequence automaton for a set of k strings of length n is Ω(n k ) for any k > 1. It solves an open problem posed by Crochemore and Tronicek [2] in 1999, in which only the case k < 2 was shown.