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On Canonical Antichains
, 1994
"... An antichain A of a wellfounded quasiorder (E, #) is canonical if for every finite subset A 0 of A, all antichains of E\{x : x # a for some a in A\A 0 } are finite. In this paper, we characterize those quasiorders that have a canonical antichain. Guoli Ding, On canonical antichains, (July ..."
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Cited by 1 (0 self)
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An antichain A of a wellfounded quasiorder (E, #) is canonical if for every finite subset A 0 of A, all antichains of E\{x : x # a for some a in A\A 0 } are finite. In this paper, we characterize those quasiorders that have a canonical antichain. Guoli Ding, On canonical antichains, (July
Longest increasing subsequences in windows based on canonical antichain partition
 In Proceedings of ISAAC
, 2005
"... Given a sequence π1π2... πn, a longest increasing subsequence (LIS) in a window π〈l, r〉 = πlπl+1... πr is a longest subsequence σ = πi1πi2... πiT such that l ≤ i1 < i2 < · · · < iT ≤ r and πi1 < πi2 < · · · < πiT. We consider the Lisw problem, which is to find the longest incre ..."
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Cited by 8 (0 self)
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increasing subsequences in a sliding window of fixedsize w over a sequence. Formally, it is to find a LIS for every window in a set SFIX = � π〈i + 1, i + w 〉 � � 0 ≤ i ≤ n − w � ∪ � π〈1, i〉, π〈n − i, n 〉 � � i < w �. By maintaining a canonical antichain partition in windows, we present an optimal
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Reduction Systems
Authorization and antichains
 University of London
, 2002
"... Access control has been an important issue in military systems for many years and is becoming increasingly important in commercial systems. There are three important access control paradigms: the BellLaPadula model, the protection matrix model and the rolebased access control model. Each of these ..."
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Cited by 18 (3 self)
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models through a rigorous mathematical approach. We examine the mathematical foundations of the rolebased access control model and conclude that antichains are a fundamental concept in the model. The analytical approach we adopt enables us to identify where improvements in the administration of role
An Antichain Algorithm for LTL Realizability
, 2009
"... In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability and synthesis problem. We show how to reduce the LTL realizability problem to a game with an observer that checks that the game visits a bounded number of times accepting states of a u ..."
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Cited by 26 (6 self)
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universal coBüchi word automaton. We show that such an observer can be made deterministic and that this deterministic observer has a nice structure which can be exploited by an incremental algorithm that manipulates antichains of game positions. We have implemented this new algorithm and our first results
Antichain Algorithms for Finite Automata
"... We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory ju ..."
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Cited by 19 (4 self)
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We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory
An Antichain Algorithm for LTL Realizability
, 2009
"... In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability problem. We show how to reduce the LTL realizability problem to a game with an observer which checks that the game visits a bounded number of times accepting states of a universal coB ..."
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Büchi word automaton. We show that such an observer can be made deterministic and that this deterministic observer has a nice structure which can be exploited by an incremental algorithm that manipulates antichains of game positions. We have implemented this new algorithm and our first results are very
Antichains and compositional algorithms for LTL synthesis
 Formal Methods in System Design
"... Abstract In this paper, we present new monolithic and compositional algorithms to solve the LTL realizability problem. Those new algorithms are based on a reduction of the LTL realizability problem to a game whose winning condition is defined by a universal automaton on infinite words with a kcoB ..."
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Cited by 13 (3 self)
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, and we show that there exists a partial order that structures the state space of the underlying safety game. This partial order can be used to define an efficient antichain algorithm. Second, we show that the algorithm can be implemented in an incremental way by considering increasing values of k
Splitting finite antichains in the homomorphism order
 ROGICS'08 RELATIONS, ORDERS AND GRAPHS: INTERACTION WITH COMPUTER SCIENCE
, 2008
"... A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that nonsplitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property fo ..."
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Cited by 2 (2 self)
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A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that nonsplitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property
ON ANTICHAINS OF SPREADING MODELS OF BANACH SPACES
, 805
"... Abstract. We show that for every separable Banach space X, either SPw(X) (the set of all spreading models of X generated by weaklynull sequences in X, modulo equivalence) is countable, or SPw(X) contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell ..."
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Abstract. We show that for every separable Banach space X, either SPw(X) (the set of all spreading models of X generated by weaklynull sequences in X, modulo equivalence) is countable, or SPw(X) contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell
Results 1  10
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