Johanna Högberg

Detecting Social Positions Using Simulation

Describing social positions and roles is an important topic within social network analysis. One approach is to compute a suitable equivalence relation on the nodes of the target network. One relation that is often used for this purpose is regular equivalence, or bisimulation, as it is known within the field of computer science. In this paper we consider a relation from computer science called simulation relation. Simulation creates a partial order on the set of actors in a network and we can use this order to identify actors that have characteristic properties. The simulation relation can also be used to compute simulation equivalence which is a less restrictive equivalence relation than regular equivalence but is still computable in polynomial time. This paper primarily considers weighted directed networks and we present definitions of both weighted simulation equivalence and weighted regular equivalence. Weighted networks can be used to model a number of network domains, including information flow, trust propagation, and communication channels. Many of these domains have applications within homeland security and in the military, where one wants to survey and elicit key roles within an organization. Identifying social positions can be difficult when the target organization lacks a formal structure or is partially hidden.

Backward and forward bisimulation minimisation of tree automata

We improve an existing bisimulation minimisation algorithm for tree automata by introducing backward and forward bisimulations and developing minimisation algorithms for them. Minimisation via forward bisimulation is also effective for deterministic automata and faster than the previous algorithm. Minimisation via backward bisimulation generalises the previous algorithm and is thus more effective but just as fast. We demonstrate implementations of these algorithms on a typical task in natural language processing.

Backward and forward bisimulation minimization of tree automata

We improve on an existing [P.A. Abdulla, J. Hogberg, L. Kaati, Bisimulation minimization of tree automata, International Journal of Foundations of Computer Science 18(4) (2007) 699-713] bisimulation minimization algorithm for finite-state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them. Minimization via forward bisimulation is also effective on deterministic tree automata, faster than the previous algorithm, and yields the minimal equivalent deterministic tree automaton. Minimization via backward bisimulation generalizes the previous algorithm and can yield smaller automata but is just as fast. We demonstrate implementations of these algorithms on a typical task in natural language processing.

Bisimulation minimization of tree automata

We extend an algorithm by Paige and Tarjan that solves the coarsest stable refinement problem to the domain of trees. The algorithm is used to minimize non-deterministic tree automata (NTA) with respect to bisimulation. We show that our algorithm has an overall complexity of

Bisimulation minimisation for weighted tree automata

O(\hat{r}m \log n)

Bisimulation Minimisation of Weighted Automata on Unranked Trees

, where

Recognizing shuffled languages

\hat{r}

Weighted unranked tree automata as a framework for plan recognition

is the maximum rank of the input alphabet, m is the total size of the transition table, and n is the number of states.

MAT learners for tree series: an abstract data type and two realizations

We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings the time complexity is slightly higher (linear instead of logarithmic in the number of states). We discuss implementations of these algorithms on a typical task in natural language processing.

An algebra for tree-based music generation

Several models of automata are available that operate unranked trees. Two well-known examples are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree automata (wsuta) and weighted parallel unranked tree automata (wputa); the qualitative automata models are reobtained by choosing the BOOLEAN semiring. The weighted versions have applications in natural language processing, XML-based data management and quantitative information retrieval. We address the minimisation problem of wsuta and wputa by using (forward and backward) bisimulations and we prove the following results: (1) for every wsuta an equivalent forward (resp. backward) bisimulation minimal wsuta can be computed in time O(mn) where n is the number of states and m is the number of transitions of the given wsuta; (2) the same result is proved for wputa instead of wsuta; (3) if the semiring is additive cancellative or the BOOLEAN semiring, then the bound can be improved to O(mlog n) for both wsuta and wputa; (4) for every deterministic puta we can compute a minimal equivalent deterministic puta in time O(mlog n); (5) the automata models wsuta, wputa, and weighted unranked tree automaton have the same computational power.