A Note Concerning the Algorithmic Analysis of Polymer Thermodynamics J. Andres Montoya Universidad Industrial de Santander jmontoya@matematicas.uis.edu.co (Received July 4, 2011) Abstract In this work we study a tally counting problem arising from a discrete model of polymer thermodynamics: The Model of Self-avoiding walks constrained to lattice strips. We show that the partition function of this model can be computed in time O ( log 2 (n) ) using a polynomial number of processors The qualitative properties of some models of statistical mechanics are completely en- coded into a discrete function called the partition function of the model [10]. Most ther- modynamical quantities describing the dynamics and structure of those models, like for example the free energy of the system, can be computed from their partition functions: solving a discrete model of statistical mechanics means computing its partition function. Most of the time partition functions are defined as counting problems [12]. We consider, in our research, a discrete model of statistical mechanics: the self-avoiding walk model. We study the computational complexity of computing the partition function of this model, we review the known facts and we prove that there exists a O ( log 2 (n) ) parallel time algorithm that computes the number of self-avoiding walks constrained to lattice strips of fixed height. The relation between self-avoiding walks and polymer chains is based on the confor- mational statistics of polymer chains, S. Edwards and his collaborators have shown that the Self-avoiding walk model can be used as the lattice model describing the relations and statements of the theory of excluded volume (much more information can be found in [3]), which is the basic thermodynamical theory of polymer space organization (see [4]). MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 67 (2012) 761-772 ISSN 0340 - 6253