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Type Checking with Open Type Functions
"... We report on an extension of Haskell with open typelevel functions and equality constraints that unifies earlier work on GADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key technical challenge of entailment checking; and w ..."
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Cited by 39 (21 self)
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We report on an extension of Haskell with open typelevel functions and equality constraints that unifies earlier work on GADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key technical challenge of entailment checking; and we give a novel, decidable, sound, and complete algorithm to solve it, together with some practicallyimportant variants. Our system is implemented in GHC, and is already in active use.
ThreeProcessor Tasks Are Undecidable
 SIAM J. Comput
, 1996
"... We show that no algorithm exists for deciding whether a finite task for three or more processors is waitfree solvable in the asynchronous readwrite sharedmemory model. This impossibility result implies that there is no constructive (recursive) characterization of waitfree solvable tasks. It also ..."
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Cited by 20 (6 self)
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We show that no algorithm exists for deciding whether a finite task for three or more processors is waitfree solvable in the asynchronous readwrite sharedmemory model. This impossibility result implies that there is no constructive (recursive) characterization of waitfree solvable tasks. It also applies to other sharedmemory models of distributed computing, such as the comparisonbased model. Key words: asynchronous distributed computation, tasksolvability, waitfree computation, contractibility problem AMS subject classification: 68Q05, 68Q22 1 Introduction A fundamental area in the theory of distributed computation is the study of asynchronous waitfree sharedmemory distributed algorithms. Characterizing the class of distributed tasks that can be solved, no matter how "inefficiently", is an important step towards a complexity theory for distributed computation. A breakthrough was the demonstation by Fisher, Lynch, and Paterson [FLP85] that certain simple tasks, such as cons...
Normalised Rewriting and Normalised Completion
, 1994
"... We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algor ..."
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Cited by 19 (2 self)
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We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm, but also the wellknown Buchberger's algorithm for computing standard bases of polynomial ideals. We investigate the particular case of completion of ground equations, In this case we prove by a uniform method that completion modulo E terminates, for some interesting E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories. We give implementation results which shows the efficiency of normalised completion with respect to completion modulo AC. 1 Introduction Equational axioms are very common in most sciences, including computer science. Equations can ...
Constantmemory validation of streaming XML documents against DTDs
 In ICDT
, 2007
"... Abstract. In this paper we investigate the problem of validating, with constant memory, streaming XML documents with respect to a DTD. Such constant memory validations can only be performed for some but not all DTDs. This paper gives a non trivial interesting step towards characterizing those DTDs ..."
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Cited by 17 (0 self)
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Abstract. In this paper we investigate the problem of validating, with constant memory, streaming XML documents with respect to a DTD. Such constant memory validations can only be performed for some but not all DTDs. This paper gives a non trivial interesting step towards characterizing those DTDs for which a constantmemory online algorithm exists. 1
The word problem for cancellation semigroups with zero
 JOURNAL OF SYMBOLIC LOGIC
, 1984
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On the singular braid monoid
, 2003
"... Abstract. Garside’s results and the existense of the greedy normal form for braids are shown to be true for the singular braid monoid. An analogue of the presentation of J. S. Birman, K. H. Ko and S. J. Lee for the braid group is also obtained for this monoid. ..."
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Cited by 6 (3 self)
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Abstract. Garside’s results and the existense of the greedy normal form for braids are shown to be true for the singular braid monoid. An analogue of the presentation of J. S. Birman, K. H. Ko and S. J. Lee for the braid group is also obtained for this monoid.
Decision problems in group theory
 Proc. London Math. Soc
, 1982
"... At the 1976 Oxford Conference, Aanderaa introduced a new class of machines which he called F machines (later renamed as modular machines). Using these he gave two remarkably short and easy examples of finitely presented groups with unsolvable word problem. Both of these examples, together with an ex ..."
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Cited by 5 (0 self)
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At the 1976 Oxford Conference, Aanderaa introduced a new class of machines which he called F machines (later renamed as modular machines). Using these he gave two remarkably short and easy examples of finitely presented groups with unsolvable word problem. Both of these examples, together with an exposition of modular
Finiteness conditions on subgroups and formal language theory
 Proc. London Math. Soc
, 1989
"... Dedicated to the memory of W. W. Boone We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersectio ..."
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Cited by 5 (1 self)
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Dedicated to the memory of W. W. Boone We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and of Griffiths by considering free reductions of languages that describe the computations of pushdown automata in one case and of Turing machines in the other, thus making clear that they are essentially the same. 1.
ORBIT DECIDABILITY AND THE CONJUGACY PROBLEM FOR SOME EXTENSIONS OF GROUPS
"... Abstract. Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A � Aut(F) is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for a ..."
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Cited by 5 (2 self)
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Abstract. Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A � Aut(F) is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form Z 2 ⋊ Fm, F2 ⋊ Fm, Fn ⋊ Z, and Z n ⋊A Fm with virtually solvable action group A � GLn(Z). Also, we give an easy way of constructing groups of the form Z 4 ⋊ Fn and F3 ⋊ Fn with unsolvable conjugacy problem. On the way, we solve the twisted conjugacy problem for virtually surface and virtually polycyclic groups, and give an example of a group with solvable conjugacy problem but unsolvable twisted conjugacy problem. As an application, an alternative solution to the conjugacy problem in Aut(F2) is given. 1.
Efficient computation in groups via compression
 In Proc. CSR 2007, LNCS 4649
, 2007
"... Abstract. A compressed variant of the word problem for finitely generated groups, where the input word is given by a contextfree grammar that generates exactly one string (also called a straightline program), is studied. It is shown that finite extensions and free products preserve the complexity ..."
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Abstract. A compressed variant of the word problem for finitely generated groups, where the input word is given by a contextfree grammar that generates exactly one string (also called a straightline program), is studied. It is shown that finite extensions and free products preserve the complexity of the compressed word problem and that the compressed word problem for a graph group can be solved in polynomial time. Using these results together with connections between the compressed word problem and the (classical) word problem allows to obtain new upper complexity bounds for certain automorphism groups and group extensions. 1