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OrderIncompleteness and Finite Lambda Models (Extended Abstract)
 Eleventh Annual IEEE Symposium on Logic in Computer Science
, 1996
"... Peter Selinger Department of Mathematics University of Pennsylvania 209 S. 33rd Street Philadelphia, PA 191046395 selinger@math.upenn.edu Abstract Many familiar models of the typefree lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about or ..."
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Cited by 8 (1 self)
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Peter Selinger Department of Mathematics University of Pennsylvania 209 S. 33rd Street Philadelphia, PA 191046395 selinger@math.upenn.edu Abstract Many familiar models of the typefree lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of fi or fijconversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the typefree lambda calculus cannot be nontrivially partially ordered. Our second result is a syntactical characterization, in terms of socalled generalized Mal'cev operators, of those lambda theories which cannot be induced by any nontrivially partially ordered model. We also consider a notion of finite models for the typefree lambda calculus. We introduce partial syntactical lambda models, which are derived from Plotkin's syntactical models of redu...
On the complexity of some Maltsev conditions
, 2006
"... Abstract. This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but th ..."
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Cited by 4 (3 self)
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Abstract. This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the size of twogenerated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity. 1.
Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms
, 1997
"... ii COPYRIGHT ..."
A CONGRUENCE IDENTITY SATISFIED BY mPERMUTABLE VARIETIES
, 2005
"... Abstract. We present a new and useful congruence identity satisfied by mpermutable varieties. It has been proved in [L1] that every mpermutable variety satisfies a nontrivial lattice identity (depending only on m). In [L2] we have found another interesting identity: Theorem 1. For m ≥ 3, every m ..."
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Abstract. We present a new and useful congruence identity satisfied by mpermutable varieties. It has been proved in [L1] that every mpermutable variety satisfies a nontrivial lattice identity (depending only on m). In [L2] we have found another interesting identity: Theorem 1. For m ≥ 3, every mpermutable variety satisfies the con] − 1 gruence identity αβh = αγh, for h = m [ m+1 2 Here, [ ] denotes integer part, and βh, γh are defined as usual: βn+1 = β + αγn, β0 = γ0 = 0, γn+1 = γ + αβn. The proof of Theorem 1 consists of two steps. As for the second step, it is an easy application of commutator theory, but in the present note we shall be concerned only with the first step. The first step is a commutatorfree proof of the following Theorem 2. If every subalgebra of A 2 is mpermutable then A satisfies (Xm). More generally: (i) If every congruence of A, thought of as a subalgebra of A 2, is mpermutable then A satisfies (Xm). (ii) If every subalgebra of A 2 generated by m + 1 elements is mpermutable then A satisfies (Xm); actually, A satisfies the stronger version of (Xm) in which α is only supposed to be a compatible relation on A, and δ is any relation on A. In the statement of Theorem 2 we have used: 2000 Mathematics Subject Classification. 08A30, 08B05. Key words and phrases. Congruence mpermutable varieties, congruence identities, HagemannMitschke’s terms.
VARIETIES WHOSE TOLERANCES ARE HOMOMORPHIC IMAGES OF THEIR CONGRUENCES GÁBOR CZÉDLI AND EMIL W. KISS
"... Dedicated to Béla Csákány on his eightieth birthday Abstract. The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsevlike condition, we characterize varieties whose tolerances are homomorphic ..."
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Dedicated to Béla Csákány on his eightieth birthday Abstract. The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsevlike condition, we characterize varieties whose tolerances are homomorphic images of their congruences (TImC). As corollaries, we prove that the variety of semilattices, all varieties of lattices, and all varieties of unary algebras have TImC. We show that a congruence npermutable variety has TImC if and only if it is congruence permutable, and construct an idempotent variety with a majority term that fails TImC. 1.
Space complexity of list Hcolouring: a dichotomy
, 2013
"... The Dichotomy Conjecture for constraint satisfaction problems (CSPs) states that every CSP is in P or is NPcomplete (FederVardi, 1993). It has been verified for conservative problems (also known as list homomorphism problems) by A. Bulatov (2003). We augment this result by showing that for digraph ..."
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The Dichotomy Conjecture for constraint satisfaction problems (CSPs) states that every CSP is in P or is NPcomplete (FederVardi, 1993). It has been verified for conservative problems (also known as list homomorphism problems) by A. Bulatov (2003). We augment this result by showing that for digraph templates H, every conservative CSP, denoted LHOM(H), is solvable in logspace or is hard for NL. More precisely, we introduce a digraph structure we call a circular N, and prove the following dichotomy: if H contains no circular N then LHOM(H) admits a logspace algorithm, and otherwise LHOM(H) is hard for NL. Our algorithm operates by reducing the lists in a complex manner based on a novel decomposition of an auxiliary digraph, combined with repeated applications of Reingold’s algorithm for undirected reachability (2005). We also prove an algebraic version of this dichotomy: the digraphs without a circular N are precisely those that admit a finite chain of polymorphisms satisfying the HagemannMitschke identities. This confirms a conjecture of Larose and Tesson (2007) for LHOM(H). Moreover, we show that the presence of a circular N can be decided in time polynomial in the size of H. 1