Computing algebraic formulas with a constant number of registers
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Context-free Handle-rewriting Hypergraph Grammars
Proceedings of the 4th International Workshop on Graph-Grammars and Their Application to Computer Science
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the expressive power of planar perfect matching and permanents of bounded treewidth matrices
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Tree-width in Algebraic Complexity
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
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Some 25 years ago Valiant introduced an algebraic model of computation in order to study the complexity of evaluating families of polynomials. The theory was introduced along with the complexity classes VP and VNP which are analogues of the classical classes P and NP. Families of polynomials that are difficult to evaluate (that is, VNP-complete) includes the permanent and hamiltonian polynomials. In a previous paper the authors together with P. Koiran studied the expressive power of permanent and hamiltonian polynomials of matrices of bounded treewidth, as well as the expressive power of perfect matchings of planar graphs. It was established that the permanent and hamiltonian polynomials of matrices of bounded treewidth are equivalent to arithmetic formulas. Also, the sum of weights of perfect matchings of planar graphs was shown to be equivalent to (weakly) skew circuits. In this paper we continue the research in the direction described above, and study the expressive power of permanents, hamiltonians and perfect matchings of matrices that have bounded pathwidth or bounded cliquewidth. In particular, we prove that permanents, hamiltonians and perfect matchings of matrices that have bounded pathwidth express exactly arithmetic formulas. This is an improvement of our previous result for matrices of bounded treewidth. Also, for matrices of bounded weighted cliquewidth we show membership in VP for these polynomials.