- e-mail:
- xpelanek(a)fi.muni.cz
- home page:
- http://www.fi.muni.cz/~xpelanek

by *
Jan Papoušek,
Vít Stanislav,
Radek Pelánek,
* April 2016, 13 pages.

**FIMU-RS-2016-02.**
Available as *Postscript*,
**PDF**.

We study the impact of question difficulty on learners’ engagement and learning using an experiment with an open online educational system for adaptive practice of geography. The experiment shows that easy questions are better for short term engagement, whereas difficult questions are better for long term engagement and learning. These results stress the necessity of careful formalization of goals and optimization criteria of open online education systems. We also present disaggregation of overall results into specific contexts of practice and highlight the issue of attrition bias. This paper is an extended version of the paper presented at Intelligent Tutoring Systems conference.

by *
Radek Pelánek,
* A full version of a paper presented at the 24th Florida Artificial Intelligence Research Society Conference January 2011, 21 pages.

**FIMU-RS-2011-01.**
Available as *Postscript*,
**PDF**.

We discuss and evaluate metrics for difficulty rating of Sudoku puzzles. The correlation coefficient with human performance for our best metric is 0.95. The data on human performance were obtained from three web portals and they comprise thousands of hours of human solving over 2000 problems. We provide a simple computational model of human solving activity and evaluate it over collected data. Using the model we show that there are two sources of problem difficulty: complexity of individual steps (logic operations) and structure of dependency among steps. Beside providing a very good Sudoku-tuned metric, we also discuss a metric with few Sudoku-specific details, which still provides good results (correlation coefficient is 0.88). Hence we believe that the approach should be applicable to difficulty rating of other constraint satisfaction problems.

by *
Petr Jarušek,
Radek Pelánek,
* April 2010, 25 pages.

**FIMU-RS-2010-01.**
Available as *Postscript*,
**PDF**.

We describe a case study in human problem solving for a particular problem - a Sokoban puzzle. For the study we collected data using the Internet. In this way we were able to collect significantly larger data (2000 problems solved, 780 hours of problem solving activity) than in typical studies of human problem solving. Our analysis of collected data focuses on the issue of problem difficulty. We show that there are very large differences in difficulty of individual Sokoban problems and that these differences are not explained by previous research. To address this gap in understanding we describe an abstract computational model of human problem solving, a metric of a problem decomposition, and formalization of a state space bottleneck. We discuss how these concepts help us understand human problem solving activity and

by *
Radek Pelánek,
Václav Rosecký,
* March 2009, 17 pages.

**FIMU-RS-2009-02.**
Available as *Postscript*,
**PDF**.

Although model checking is usually described as an automatic technique, the verification process with the use of model checker is far from being fully automatic. With the aim of automating the verification process, we elaborate

by *
Radek Pelánek,
Václav Rosecký,
Jaroslav Šeděnka,
* February 2008, 19 pages.

**FIMU-RS-2008-02.**
Available as *Postscript*,
**PDF**.

We study two techniques for reducing memory consumption of explicit model checking - state caching and state compression. In order to evaluate these techniques we review the literature, discuss trends in relevant research, and

by *
Radek Pelánek,
Pavel Šimeček,
* January 2008, 21 pages.

**FIMU-RS-2008-01.**
Available as *Postscript*,
**PDF**.

We introduce the problem of estimation of state space parameters, argue that it is an interesting and practically relevant problem, and study several simple estimation techniques. Particularly, we focus on estimation of the number of reachable states. We study techniques based on sampling of the state space and techniques that employ data mining techniques (classification trees, neural networks) over parameters of breadth-first search. We show that even through the studied techniques are not able to produce exact estimates, it is possible to obtain useful information about a state space by sampling and to use this information to automate the verification process.

by *
Radek Pelánek,
* October 2006, 39 pages.

**FIMU-RS-2006-03.**
Available as *Postscript*,
**PDF**.

We present BEEM - BEnchmarks for Explicit Model checkers. This benchmark set includes more than 50 models together with correctness properties (both safety and liveness). The benchmark set is accompanied by an comprehensive web

The report describes the rationale beyond the form of the benchmark set, the design of the web portal and the main aspects of its realization, and also an example of an experimental analysis over the benchmark set: an analysis of a performance of sequential and distributed reachability.

The address of the web portal is http://anna.fi.muni.cz/models .

by *
Pavel Krčál,
Radek Pelánek,
* A full version of the paper presented at conference FSTTCS 2005. December 2005, 31 pages.

**FIMU-RS-2005-09.**
Available as *Postscript*,
**PDF**.

Timed systems can be considered with two types of semantics -- dense time semantics and discrete time semantics. The most typical examples of both of them are real semantics and sampled semantics (i.e., discrete semantics with a fixed time step epsilon). In this work, we study different

by *
Radek Pelánek,
* February 2005, 22 pages.

**FIMU-RS-2005-03.**
Available as *Postscript*,
**PDF**.

We present an overview of equivalences of finite state structures and discuss methods for computing reduced structures on-the-fly. We evaluate merits of these reductions on a large set of model checking case studies. It turns out that the achieved reduction can be significant, but that it is not so ``drastic" as sometimes claimed in the literature. We also propose some new reduction methods.

by *
Radek Pelánek,
Jan Strejček,
* September 2004, 26 pages.

**FIMU-RS-2004-08.**
Available as *Postscript*,
**PDF**.

It is known that Linear Temporal Logic (LTL) has the same expressive power as alternating 1-weak automata (A1W automata, also called alternating linear automata or very weak alternating automata). A translation of LTL formulae

by *
Ivana Černá,
Radek Pelánek,
* April 2003, 18 pages.

**FIMU-RS-2003-03.**
Available as *Postscript*,
**PDF**.

The hierarchy of properties as overviewed by Manna and Pnueli relates language,

by *
Ivana Černá,
Radek Pelánek,
* December 2002, 24 pages.

**FIMU-RS-2002-09.**
Available as *Postscript*,
**PDF**.

The fair cycle detection problem is at the heart of both LTL and fair

by *
Luboš Brim,
Ivana Černá,
Pavel Krčál,
Radek Pelánek,
* This is a full version of the paper presented at SOFSEM 2001. November 2001, 22 pages.

**FIMU-RS-2001-09.**
Available as *Postscript*,
**PDF**.

A distributed algorithm for the single-source shortest path problem for directed graphs with arbitrary edge lengths is proposed. The new algorithm is based on relaxations and uses reverse search for inspecting edges and thus avoids using any additional data structures. At the same time the algorithm uses a novel way to recognize a reachable negative-length cycle in the graph which facilitates the scalability of the algorithm.

by *
Luboš Brim,
Ivana Černá,
Pavel Krčál,
Radek Pelánek,
* This is a full version of the paper presented at FST&TCS 2001. May 2001, 19 pages.

**FIMU-RS-2001-01.**
Available as *Postscript*,
**PDF**.

A distributed algorithm for single source shortest path