TY - COMP
TI - dmurfet/2simplicialtransformer
AU - Murfet, Daniel
AB - Code for the 2-simplicial Transformer paper. Contribute to dmurfet/2simplicialtransformer development by creating an account on GitHub.
DA - 2019/10/14/T08:10:47Z
PY - 2019
DP - GitHub
LA - Python
UR - https://github.com/dmurfet/2simplicialtransformer
Y2 - 2019/11/22/16:50:05
KW - Abstract machines
KW - Algebra
KW - Implementation
KW - Machine learning
KW - Semantics
ER -
TY - JOUR
TI - Logic and the $2$-Simplicial Transformer
AU - Murfet, Daniel
AU - Clift, James
AU - Doryn, Dmitry
AU - Wallbridge, James
T2 - arXiv:1909.00668 [cs, stat]
AB - We introduce the $2$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.
DA - 2019/09/02/
PY - 2019
DP - arXiv.org
UR - http://arxiv.org/abs/1909.00668
Y2 - 2019/11/21/20:31:14
KW - Abstract machines
KW - Algebra
KW - Machine learning
KW - Semantics
ER -
TY - JOUR
TI - Influence Networks Compared with Reaction Networks: Semantics, Expressivity and Attractors
AU - Fages, Francois
AU - Martinez, Thierry
AU - Rosenblueth, David A.
AU - Soliman, Sylvain
T2 - IEEE/ACM Trans. Comput. Biol. Bioinformatics
AB - Biochemical reaction networks are one of the most widely used formalisms in systems biology to describe the molecular mechanisms of high-level cell processes. However, modellers also reason with influence diagrams to represent the positive and negative influences between molecular species and may find an influence network useful in the process of building a reaction network. In this paper, we introduce a formalism of influence networks with forces, and equip it with a hierarchy of Boolean, Petri net, stochastic and differential semantics, similarly to reaction networks with rates. We show that the expressive power of influence networks is the same as that of reaction networks under the differential semantics, but weaker under the discrete semantics. Furthermore, the hierarchy of semantics leads us to consider a positive Boolean semantics that cannot test the absence of a species, that we compare with the negative Boolean semantics with test for absence of a species in gene regulatory networks à la Thomas. We study the monotonicity properties of the positive semantics and derive from them an algorithm to compute attractors in both the positive and negative Boolean semantics. We illustrate our results on models of the literature about the p53/Mdm2 DNA damage repair system, the circadian clock, and the influence of MAPK signaling on cell-fate decision in urinary bladder cancer.
DA - 2018/07//
PY - 2018
DO - 10/ggdf94
DP - ACM Digital Library
VL - 15
IS - 4
SP - 1138
EP - 1151
SN - 1545-5963
ST - Influence Networks Compared with Reaction Networks
UR - https://doi.org/10.1109/TCBB.2018.2805686
Y2 - 2019/11/23/07:40:24
KW - Biology
KW - Rewriting theory
KW - Symbolic logic
KW - Systems biology
ER -
TY - JOUR
TI - BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge
AU - Fages, F.
AU - Calzone, L.
AU - Soliman, S.
T2 - Bioinformatics
DA - 2006/07/15/
PY - 2006
DO - 10/dfv
DP - Crossref
VL - 22
IS - 14
SP - 1805
EP - 1807
LA - en
SN - 1367-4803, 1460-2059
ST - BIOCHAM
UR - https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btl172
Y2 - 2019/11/23/07:28:51
KW - Abstract machines
KW - Biology
KW - Implementation
KW - Rewriting theory
KW - Symbolic logic
KW - Systems biology
ER -
TY - JOUR
TI - Domain theory, testing and simulation for labelled Markov processes
AU - van Breugel, Franck
AU - Mislove, Michael
AU - Ouaknine, Joël
AU - Worrell, James
T2 - Theoretical Computer Science
T3 - Foundations of Software Science and Computation Structures
AB - This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes (LMPs). The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. In general, LMPs are not required to satisfy a finite-branching condition—indeed the state space may be a continuum, with the transitions given by arbitrary probability measures. Nevertheless we show that to characterize bisimilarity it suffices to use finitely-branching labelled trees as tests. Our results involve an interaction between domain theory and measure theory. One of the main technical contributions is to show that a final object in a suitable category of LMPs can be constructed by solving a domain equation D≅V(D)Act, where V is the probabilistic powerdomain. Given an LMP whose state space is an analytic space, bisimilarity arises as the kernel of the unique map to the final LMP. We also show that the metric for approximate bisimilarity introduced by Desharnais, Gupta, Jagadeesan and Panangaden generates the Lawson topology on the domain D.
DA - 2005/03/01/
PY - 2005
DO - 10/ft9vc5
DP - ScienceDirect
VL - 333
IS - 1
SP - 171
EP - 197
J2 - Theoretical Computer Science
LA - en
SN - 0304-3975
UR - http://www.sciencedirect.com/science/article/pii/S030439750400711X
Y2 - 2019/11/26/19:59:13
KW - Coalgebras
KW - Denotational semantics
KW - Probabilistic transition systems
KW - Transition systems
ER -
TY - JOUR
TI - Bisimulation for Labelled Markov Processes
AU - Desharnais, Josée
AU - Edalat, Abbas
AU - Panangaden, Prakash
T2 - Information and Computation
AB - In this paper we introduce a new class of labelled transition systems—labelled Markov processes— and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete. We assume that the state space is a certain type of common metric space called an analytic space. We show that our definition of probabilistic bisimulation generalizes the Larsen–Skou definition given for discrete systems. The formalism and mathematics is substantially different from the usual treatment of probabilistic process algebra. The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. This study revealed some unexpected results, even for discrete probabilistic systems. •Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition.•We do not need any finite branching assumption, yet there is no need of infinitary conjunction. We also show how to construct the maximal autobisimulation on a system. In the finite state case, this is just a state minimization construction. The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts about analytic spaces and appear, at first sight, to be entirely nonconstructive. Yet one can give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.
DA - 2002/12/15/
PY - 2002
DO - 10/fmp9vd
DP - ScienceDirect
VL - 179
IS - 2
SP - 163
EP - 193
J2 - Information and Computation
LA - en
SN - 0890-5401
UR - http://www.sciencedirect.com/science/article/pii/S0890540101929621
Y2 - 2019/11/26/21:27:24
KW - Coalgebras
KW - Denotational semantics
KW - Probabilistic transition systems
KW - Symbolic logic
KW - Transition systems
ER -