Work packages

WP1no picture
Work package number 1 Work package title Mathematical tools: matrix computations and matrix equations and inequations solving
Lead SRO's acronym UNFSM, FTSC
WP Coordinator - team member's ID P1 - Predrag Stanimirović
Team member's ID PI, P1, P2, P3, P7, P8, P9

Objectives: The main objective of this work package is to provide the necessary mathematical tools for use in other work packages. This will be achieved through completion of the following specific aims:

  • development of general methods for solving equations and inequations in certain abstract algebraic structures, such as semigroups, partially ordered sets and complete lattices,
  • development of methods and algorithms for solving different types of systems of equations and inequations that involve fuzzy matrices, max-plus matrices and matrices over the field of real numbers,
  • development of methods and algorithms for factorization of fuzzy matrices, max-plus matrices and matrices over the field of reals, as well as methods for testing the existence and algorithms for computing generalized inverses of these types of matrices.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Equations and inequations solving in abstract algebraic structures - that encompasses studying methods of solving equations and representations of generalized inverses in semigroups (to be performed by PI, P1, P2 and P9), as well as studying methods of solving inequations and equations defined by residuated functions on partially ordered sets and complete lattices (by PI and P2);
  • Developing theory and algorithms for solving systems of matrix equations and inequations - that will be done for different types of equations and inequations involving fuzzy matrices (by PI, P2 and P8), as well as for those involving max-plus matrices (by PI and P3) and real matrices (by PI, P1 and P7);
  • Developing theory and algorithms for matrix factorizations and computing generalized inverses - that involves the study of matrix factorizations and generalized inverses for fuzzy matrices (to be performed by PI, P2, P3 and P9), max-plus matrices (by PI, P2 and P3), and real matrices (by PI, P1 and P7).
WP2no picture
Work package number 2 Work package title Semantics and representations of WFAs
Lead SRO's acronym UNFSM, FTSC, FSUKG
WP Coordinator - team member's ID P4 - Nada Damljanović
Team member's ID PI, P2, P4, P13

Objectives: The main objective of WP2 is to consider some theoretical issues concerning semantics and representations of WFAs over semirings and strong bimonoids, which will play an important role in the considerations within other WPs. This will be achieved through completion of the following specific aims:

  • study of linear representations of WFAs, Nerode and reverse Nerode automata,
  • study of linear and nonlinear weighted automata and related concepts,
  • study of different semantics for WFAs, weighted context-free grammars and weighted pushdown automata over strong bimonoids,
  • study of coalgebraic representations of WFAs.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Semantics and representations of WFAs over semirings - this encompasses the study of linear representations of WFAs, linear and nonlinear weighted automata and and their relationships, and related concepts (to be performed by PI, P2, P4 and P13);
  • Semantics in the absence of distributivity - this encompasses the study of different semantics for WFAs, weighted context-free grammars and weighted pushdown automata over strong bimonoids (to be performed by PI, P2 and P4);
  • Coalgebraic semantics for WFAs - this encompasses the study of coalgebraic semantics and representations of weighted finite automata (to be performed by PI, P2, P4 and P13).
WP3no picture
Work package number 3 Work package title Simulation and bisimulation algorithms
Lead SRO's acronym UNFSM, FTSC, FSUKG , UNFPV
WP Coordinator - team member's ID P6 - Ivana Micić
Team member's ID PI, P2, P3, P4, P5, P6, P8, P9, P11, P12

Objectives: The main objective of WP3 is to develop a general theory of simulation and bisimulation matrices for WFAs over semirings based on solving particular systems of matrix inequations and equations disscussed in the description of WP1. This general aim will be achieved through completion of the set of specific objectives that include:

  • development of algorithms for testing the existence and computation of simulations and bisimulations for different types of WFAs,
  • development of algorithms for testing the existence and computation of approximate simulations and bisimulations for the same types of automata,
  • transfer of the methodology originally intended for automata into the social network analysis and to many-valued modal logics.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Developing theory and algorithms for testing the existence and computing simulations and bisimulations - this will be done for max-plus automata (by PI, P3 and P11) and for WFAs over the field of reals (by PI, P2, P4 and P11);
  • Developing theory and algorithms for testing the existence and computing approximate simulations and bisimulations - this will be done for fuzzy automata (by PI, P6 and P9), for max-plus automata (by PI, P3 and P11), and for WFAs over the field of reals (by PI, P2, P4 and P11);
  • Transfer of methodology to weighted social networks and many-valued modal logics - the methodology originally intended for automata will be modified to be used to develop theory and algorithms for testing the existence and computing simulations and bisimulations between weighted social networks (to be performed by PI, P2, P5, P6, P8 and P9) and between models of many-valued modal logics (to be performed by PI, P2 and P12).
WP4no picture
Work package number 4 Work package title State reduction and minimization algorithms
Lead SRO's acronym UNFSM
WP Coordinator - team member's ID P3 - Aleksandar Stamenković
Team member's ID PI, P1, P2, P3, P6, P7, P9, P11

Objectives: The main objective of WP4 is to develop a general theory of state reduction and approximate state reduction of WFAs over semirings based on solving particular systems of matrix inequations and equations disscussed in the description of WP1, as well as minimization and approximate minimization of such types of automata. This general aim will be achieved through completion of the set of specific objectives that include:

  • development of theory and algorithms for state reduction of different types of WFAs,
  • development of theory and algorithms for approximate state reduction of the same types of WFAs,
  • development of theory and algorithms of minimization of the same types of WFAs,
  • development of theory and algorithms for approximate minimization of the same types of WFAs.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Developing theory and algorithms for state reduction and approximate state reduction of WFAs - that will be done for fuzzy automata (by PI, P3, P6 and P9), for max-plus automata (by PI, P3, P6, P9 and P11), and for WFAs over the field of reals (by PI, P1, P2 and P7);
  • Developing theory and algorithms for minimization and approximate minimization of WFAs - that will be done for fuzzy automata (by PI, P3, P6 and P9), for max-plus automata (by PI, P3, P6, P9 and P11), and for WFAs over the field of reals (by PI, P1, P2 and P7).
WP5no picture
Work package number 5 Work package title Determinization algorithms
Lead SRO's acronym UNFSM
WP Coordinator - team member's ID P5 - Zorana Jančić
Team member's ID PI, P2, P3, P4, P5, P6, P9, P10, P13

Objectives: The general objective of this work package is to develop methods and algorithms for the determinization, approximate determinization and canonization of WFAs over semirings. This will be achieved through completion of the following specific goals:

  • development of new methods and algorithms for determinization of different types of WFAs,
  • development of theory and algorithms for approximate determinization of the same types of WFAs,
  • development of theory and algorithms for canonization of the same types of WFAs.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Developing new methods and algorithms for determinization of WFAs - this will be done for fuzzy automata (by PI, P5, P6 and P9), for max-plus automata (by PI, P3, P5, P9 and P10), and for WFAs over the field of reals (by PI, P2, P9 and P10);
  • Developing theory and algorithms for approximate determinization of WFAs - this will be done for fuzzy automata (by PI, P5, P6 and P9), max-plus automata (by PI, P3, P5, P9 and P10), and WFAs over the field of reals (by PI, P2, P4, P9, P10 and P13);
  • Developing theory and algorithms for canonization of WFAs - this will be done for fuzzy automata (by PI, P5, P6 and P9), max-plus automata (by PI, P3, P5, P9 and P10), and WFAs over the field of reals (by PI, P2, P4, P9, P10 and P13).
WP6no picture
Work package number 6 Work package title Reconstruction algorithms
Lead SRO's acronym UNFSM
WP Coordinator - team member's ID P2 - Jelena Ignjatović
Team member's ID PI, P1, P2, P3, P4, P5, P7, P11

Objectives: The general objective of this work package is to develop theory and algorithms for reconstruction of WFAs from their behaviours, and to develop theory and algorithms for learning WFAs. This will be done by achieving the following specific objectives:

  • developing new methods and algorithms for reconstruction of WFAs from word functions they compute,
  • developing methods and algorithms for reconstruction of WFAs with output from sequential weighted input-output transformations they perform,
  • developing methods and algorithms for learning WFAs and WFAs with output.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Developing theory and algorithms for reconstruction of WFAs - so far the reconstruction of automata from the word functions they compute has been studied in detail for WFAs over the field of real numbers, and here some new results will be provided concerning that issue (by PI, P1, P2, P4, P7 and P11), and the same issue will also be considered in the context of fuzzy automata (by PI, P2 and P5) and in the context of max-plus automata (by PI, P2, P3 and P11);
  • Developing theory and algorithms for reconstruction of WFAs with output - the problem of reconstructing WFAs with output from the sequential weighted input-output transformations they perform will be considered for fuzzy automata (by PI, P2 and P5), for max-plus automata (by PI, P2, P3 and P11), and for WFAs over the field of reals (by PI, P1, P2, P7 and P11);
  • Developing theory and algorithms for learning WFAs - design of learning algorithms for WFAs will be done, as well as their implementation and testing in approximation of machine learning models for sequence processing. It will be worked primarily with WFAs over the field of real numbers and probabilistic automata (researchers PI, P2 and P11), and it is also planned to discuss related issues for fuzzy automata and max-plus automata.
WP7no picture
Work package number 7 Work package title Project management and dissemination
Lead SRO's acronym UNFSM
WP Coordinator - team member's ID PI - Miroslav Ćirić
Team member's ID PI, P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13

Objectives: The objective of this work package is to manage all Project activities (research, financial, administrative, dissemination) in a way to ensure that they are realized within the deadlines provided by the Project proposal and in compliance with the law and the agreed conditions and obligations. In addition, the goal is to ensure the promotion and visibility of Project results.

Description of work and role of the team members


The work on this work package will be done through the following subactivities:

  • Management of research activities - Regular monitoring of the implementation of research activities on the Project will be carried out. Once a month (and more often, if necessary), Project team meetings will be held at which WP coordinators will report on progress of research activities. With the participation of all members of the Project team, guidelines for improving the work on the Project and overcoming possible problems will be adopted. Team member P9 will assist PI in managing the research activities and writing the scientific parts of reports, while P11 will provide technical support;
  • Management of financial and other activities - The expenditure from the Project budget will be regularly monitored and the required documentation will be collected. PI will ensure that the use of funds is in accordance with the law and the agreed conditions and obligations. In the financial management of the Project, PI will be assisted by P2, who has significant experience in managing Erasmus + CBHE projects. They will also perform management of administrative activities and risk management;
  • Management and implementation of dissemination activities - In organizing and monitoring the implementation of dissemination activities PI will be assisted by P3. All Project team members will be in charge of implementing various dissemination activities at their institutions and outside them, in the way described in Section 2.2. In particular, P8, P9 and P10 will be in charge of creating the Project website, while P6 and P10 will be in charge of promoting the Project in mainstream and social media.