Outputs (66)

Constraint satisfaction, logic and forbidden patterns (2007)
Journal Article
Madelaine, F., & Stewart, I. (2007). Constraint satisfaction, logic and forbidden patterns. SIAM Journal on Computing, 37(1), 132-163. https://doi.org/10.1137/050634840

In the early nineties, Feder and Vardi attempted to find a large sub-class of NP which exhibits a dichotomy; that is, where every problem in the sub-class is either solvable in polynomial-time or NP-complete. Their studies resulted in a candidate cla... Read More about Constraint satisfaction, logic and forbidden patterns.

An infinite hierarchy in a class of polynomial-time program schemes (2006)
Journal Article
Gault, R., & Stewart, I. (2006). An infinite hierarchy in a class of polynomial-time program schemes. Theory of Computing Systems, 39(5), 753-783. https://doi.org/10.1007/s00224-005-1230-6

We define a class of program schemes RFDPS constructed around notions of forall-loops, repeat-loops, arrays and if-then-else instructions, and which take finite structures as inputs, and we examine the class of problems, denoted RFDPS also, accepted... Read More about An infinite hierarchy in a class of polynomial-time program schemes.

The computational complexity of the parallel knock-out problem (2006)
Presentation / Conference Contribution
Broersma, H., Johnson, M., Paulusma, D., & Stewart, I. (2006, March). The computational complexity of the parallel knock-out problem. Presented at 7th Latin American Theoretical Informatics Symposium (LATIN 2006), Valdivia, Chile

We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for... Read More about The computational complexity of the parallel knock-out problem.

Dichotomies for classes of homomorphism problems involving unary functions (2004)
Journal Article
Feder, T., Madelaine, F., & Stewart, I. (2004). Dichotomies for classes of homomorphism problems involving unary functions. Theoretical Computer Science, 314(1-2), 1-43. https://doi.org/10.1016/j.tcs.2003.12.015

We study non-uniform constraint satisfaction problems where the underlying signature contains constant and function symbols as well as relation symbols. Amongst our results are the following. We establish a dichotomy result for the class of non-unifo... Read More about Dichotomies for classes of homomorphism problems involving unary functions.

The complexity of achievement and maintenance problems in agent-based systems (2003)
Journal Article
Stewart, I. (2003). The complexity of achievement and maintenance problems in agent-based systems. Artificial Intelligence, 146(2), 175-191. https://doi.org/10.1016/s0004-3702%2803%2900014-6

We completely classify the computational complexity of the basic achievement and maintenance agent design problems in bounded environments when these problems are parameterized by the number of environment states and the number of agent actions. The... Read More about The complexity of achievement and maintenance problems in agent-based systems.

Some problems not definable using structure homomorphisms (2003)
Journal Article
Madelaine, F., & Stewart, I. (2003). Some problems not definable using structure homomorphisms. Ars combinatoria, 67, 153-159

We exhibit some problems definable in Feder and Vardi's logic MMSNP that are not in the class CSP of constraint satisfaction problems. Whilst some of these problems have previously been shown to be in MMSNP (that is, definable in MMSNP) but not in CS... Read More about Some problems not definable using structure homomorphisms.

Using program schemes to capture polynomial-time logically on certain classes of structures (2003)
Journal Article
Stewart, I. (2003). Using program schemes to capture polynomial-time logically on certain classes of structures. LMS journal of computation and mathematics, 6, 40-67

We continue the study of the expressive power of certain classes of program schemes on finite structures, in relation to more mainstream logics studied in finite model theory and to computational complexity. We show that there exists a program scheme... Read More about Using program schemes to capture polynomial-time logically on certain classes of structures.

Greedy algorithms, H-colourings and a complexity-theoretic dichotomy (2003)
Journal Article
Puricella, A., & Stewart, I. (2003). Greedy algorithms, H-colourings and a complexity-theoretic dichotomy. Theoretical Computer Science, 290(3), 1897-1913. https://doi.org/10.1016/s0304-3975%2802%2900329-8

Let H be a fixed undirected graph. An H-colouring of an undirected graph G is a homomorphism from G to H. If the vertices of G are partially ordered then there is a generic non-deterministic greedy algorithm which computes all lexicographically first... Read More about Greedy algorithms, H-colourings and a complexity-theoretic dichotomy.

A note on first-order projections and games (2003)
Journal Article
Arratia, A., & Stewart, I. (2003). A note on first-order projections and games. Theoretical Computer Science, 290(3), 2085-2093. https://doi.org/10.1016/s0304-3975%2802%2900491-7

We show how the fact that there is a first-order projection from the problem TC (transitive closure) to some other problem $\Omega$ enables us to automatically deduce that a natural game problem, $\mathcal{LG}(\Omega)$, whose instances are labelled i... Read More about A note on first-order projections and games.

Program schemes, arrays, Lindström quantifiers and zero-one laws (2002)
Journal Article
Stewart, I. (2002). Program schemes, arrays, Lindström quantifiers and zero-one laws. Theoretical Computer Science, 275(1-2), 283-310. https://doi.org/10.1016/s0304-3975%2801%2900183-9

We characterize the class of problems accepted by a class of program schemes with arrays, NPSA, as the class of problems defined by the sentences of a logic formed by extending first-order logic with a particular uniform (or vectorized) sequence of L... Read More about Program schemes, arrays, Lindström quantifiers and zero-one laws.