Formal Methods

At RISC we understand by formal methods the application of methods from symbolic computation (especially from formal logic) to rigorously reason about properties of computer programs, in particular to verify their correctness with respect to a specification.

The term "formal methods" applies to all techniques that make computer software and computing systems subject to formal reasoning. By treating a computer program as a mathematical object with a formal semantics, we can rigorously argue about its behavior, e.g., why it always computes the correct result; this reasoning can be supported or even automated by corresponding software. Formal methods are industrially applied wherever computer/program failures are not acceptable, e.g. to mission-critical software, computer chips, or communication protocols.

Formal methods comprise at least two aspects:

  1. "Specification" means to describe the expected behavior of a program in a mathematically precise way (e.g. as a logic formula, see the "ensures" clause in the attached picture which gives the specification of a program).
  2. "Verification": means to demonstrate with mathematical rigor that every possible execution of the program does not crash and indeed satisfies its specification, preferably with computer support (by reasoners that apply proof-based techniques or by model checkers that investigate the space of all possible executions).

Furthermore, the "Validation" of a specification aims to ensure that this specification actually describes the intended behavior; thus the verification of a program with respect to this specification indeed demonstrates that the program satisfies the properties that we are interested in.

Even if the complete verification of a program may sometimes not be feasible, a "light-weight" application of formal methods may help to increase our confidence in the correctness of a program:

  • "Extended Static Checking" and "Bounded Model Checking" apply logic-based techniques to detect errors in a program; while these techniques do not necessarily ensure that a program is correct (they falsify a program rather than verifying it), they at least raise its quality;
  • "Runtime Verification" supervises the execution of a program by an automatically generated monitor that triggers a warning if the program violates its specification; while this does not rule out possible future errors, it at least ensures that the execution so far has been correct.

The support respectively automation of all these aspects by software (automated program verifiers, interactive verification assistants, model checkers, static program analyzers, specification analyzers) is a hot topic of research.

Software

RISC ProgramExplorer

An Interactive Program Reasoning Environment

The RISC ProgramExplorer is a computer-supported program reasoning environment for a simple imperative programming language "MiniJava"; it incorporates the RISC ProofNavigator as a semi-automatic proving assistant. The environment has been developed mainly for educational purposes (see this paper for a ...

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RISC ProofNavigator

An Interactive Proof Assistant for Program/System Verification

The RISC ProofNavigator is an interactive proof assistant for supporting formal reasoning about computer programs and computing systems, see the README file and this short paper for the main ideas; it is the core reasoning component of the RISC ProgramExplorer. ...

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RISCAL

The RISC Algorithm Language: A Language and Associated Software System for Specifying and Verifying Mathematical Algorithms

The RISC Algorithm Language (RISCAL) is a specification language and associated software system for describing mathematical algorithms, formally specifying their behavior based on mathematical theories, and validating the correctness of algorithms, specifications, and theories by execution/evaluation. The software has been ...

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Publications

2021

[Reichl]

Semantic Evaluation versus SMT Solving in the RISCAL Model Checker

Wolfgang Schreiner, Franz-Xaver Reichl

Technical report no. 21-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). June 2021. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6328,
author = {Wolfgang Schreiner and Franz-Xaver Reichl},
title = {{Semantic Evaluation versus SMT Solving in the RISCAL Model Checker}},
language = {english},
abstract = {In this paper, we compare two alternative mechanisms for deciding the validity of first-order formulas over finite domains supported by the mathematical model checker RISCAL: first, the original built-in approach of “semantic evaluation” (based on an implementation of the denotational semantics of the RISCAL language) and, second, the later implemented approach of SMT solving (based on satisfiability preserving translations of RISCAL formulas to formulas in the SMT-LIB logic QF_UFBV, respectively to quantified SMT-LIB bitvector formulas). After a short presentation of the two approaches and a discussion oftheir fundamental pros and cons, we quantitatively evaluate them, both by a set of artificial benchmarks and by a set of benchmarks taken from real-life applications of RISCAL; for this, we apply the state-of-the-art SMT solvers Boolector, CVC4, Yices, and Z3. Our benchmarks demonstrate that (while SMT solving generally vastly outperforms semantic evaluation), the various SMT solvers exhibit great performance differences. More important, our investigations also identify some classes of formulas where semantic evaluation is able to compete with (or even outperform) satisfiability solving, outlining some room forimprovements in the translation of RISCAL formulas to SMT-LIB formulas as well as in the current SMT technology.},
number = {21-11},
year = {2021},
month = {June},
keywords = {model checking, satisfiability solving, formal specification, formal verficiation},
sponsor = {JKU Linz Institute of Technology (LIT) Project LOGTECHEDU, Aktion Österreich- Slowakei Project 2019-10-15-003, Austrian Science Fund (FWF) grant W1255.},
length = {30},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[STUDENT]

Refinement Types for Elm

Lucas Payr

Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. Master Thesis. April 2021. Also available as RISC report no. 21-10. Master Thesis. [pdf]
[bib]
@misc{RISC6304,
author = {Lucas Payr},
title = {{Refinement Types for Elm}},
language = {english},
abstract = {The aim of this thesis is to add refinement types to Elm. Elm is a pure functionalprogramming language that uses a Hindley-Miler type system. Refinement types aresubtypes of existing types. These subtypes are defined by a predicate that specifieswhich values are part of the subtypes. To extend a Hindley-Miler type system, onecan use so-called liquid types. These are special refinement types that come with analgorithm for type inference. This algorithm interacts with an SMT solver to solvesubtyping conditions. A type system using liquid types is not complete, meaning notevery valid program can be checked. Instead, liquid types are only defined for a subsetof expressions and only allow specific predicates. In this thesis, we give a formaldefinition of the Elm language and its type system. We extend the type system withliquid types and provide a subset of expressions and a subset of predicates such thatthe extended type system is sound. We use the free software system “K Framework”for rapid prototyping of the formal Elm type system. For rapid prototyping of thecore algorithm of the extended type system we implemented said algorithm in Elmand checked the subtyping condition in Microsoft’s SMT solver Z3.},
year = {2021},
month = {April},
note = {Also available as RISC report no. 21-10},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal semantics, formal type systems, programming languages, satisfiability solving},
length = {135},
type = {Master Thesis}
}

2020

[Cerna]

Idempotent Anti-unification

David Cerna, Temur Kutsia

ACM Transactions on Computational Logic (TOCL) 21(2), pp. 10:1-10:32. 2020. ACM Press, ISSN 1529-3785. [doi] [pdf]
[bib]
@article{RISC6023,
author = {David Cerna and Temur Kutsia},
title = {{Idempotent Anti-unification}},
language = {english},
journal = {ACM Transactions on Computational Logic (TOCL)},
volume = {21},
number = {2},
pages = {10:1--10:32},
publisher = {ACM Press},
isbn_issn = {ISSN 1529-3785},
year = {2020},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1145/3359060}
}
[Cerna]

Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App

David M. Cerna, Martina Seidl, Wolfgang Schreiner, Wolfgang Windsteiger, Armin Biere

In: ITICSE 2020, ACM (ed.), Proceedings of ITICSE, pp. 61-67. 2020. 9781450368742. [doi]
[bib]
@inproceedings{RISC6096,
author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},
title = {{Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App}},
booktitle = {{ITICSE 2020}},
language = {english},
abstract = {In this paper, we share our experiences concerning the introduc-tion of the Android-based self-study app AXolotl within the first-semester logic course offered at our university. This course is manda-tory for students majoring in Computer Science and Artificial In-telligence. AXolotl was used as part of an optional lab assignmentbridging clausal reasoning and SAT solving with classical reason-ing, proof construction, and first-order logic. The app provides anintuitive interface for proof construction in various logical calculiand aids the students through rule application. The goal of thelab assignment was to help students make a smoother transitionfrom clausal and decompositional reasoning used earlier in thecourse to inferential and contextual reasoning required for proofconstruction and first-order logic. We observed that the lab had apositive influence on students’ understanding and end the paperwith a discussion of these results.},
pages = {61--67},
isbn_issn = {9781450368742},
year = {2020},
editor = {ACM},
refereed = {yes},
length = {7},
conferencename = {ITICSE},
url = {https://dl.acm.org/doi/10.1145/3341525.3387409}
}
[Cerna]

Computational Logic in the First Semester of Computer Science: An Experience Report

David M. Cerna, Martina Seidl, Wolfgang Schreiner, Wolfgang Windsteiger, Armin Biere

In: Proceedings of the 12th International Conference on Computer Supported Education - Volume 2: CSEDU, Springer (ed.), Proceedings of CSEDU, pp. 374-381. 2020. 978-989-758-417-6. [doi]
[bib]
@inproceedings{RISC6097,
author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},
title = {{Computational Logic in the First Semester of Computer Science: An Experience Report}},
booktitle = {{Proceedings of the 12th International Conference on Computer Supported Education - Volume 2: CSEDU}},
language = {english},
abstract = {Nowadays, logic plays an ever-increasing role in modern computer science, in theory as well as in practice.Logic forms the foundation of the symbolic branch of artificial intelligence and from an industrial perspective,logic-based verification technologies are crucial for major hardware and software companies to ensure thecorrectness of complex computing systems. The concepts of computational logic that are needed for such purposes are often avoided in early stages of computer science curricula. Instead, classical logic education mainlyfocuses on mathematical aspects of logic depriving students to see the practical relevance of this subject. Inthis paper we present our experiences with a novel design of a first-semester bachelor logic course attendedby about 200 students. Our aim is to interlink both foundations and applications of logic within computerscience. We report on our experiences and the feedback we got from the students through an extensive surveywe performed at the end of the semester.},
pages = {374--381},
isbn_issn = {978-989-758-417-6},
year = {2020},
editor = {Springer},
refereed = {yes},
length = {8},
conferencename = {CSEDU},
url = {https://www.scitepress.org/Link.aspx?doi=10.5220/0009464403740381}
}
[Cerna]

Unital Anti-Unification: Type and Algorithms

David M. Cerna, Temur Kutsia

In: Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020), Zena M. Ariola (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 167, pp. 26:1-26:20. 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, ISBN 978-3-95977-155-9, ISSN 1868-8969. [url]
[bib]
@inproceedings{RISC6132,
author = {David M. Cerna and Temur Kutsia},
title = {{Unital Anti-Unification: Type and Algorithms}},
booktitle = {{Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {167},
pages = {26:1--26:20},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum für Informatik},
isbn_issn = {ISBN 978-3-95977-155-9, ISSN 1868-8969},
year = {2020},
editor = {Zena M. Ariola},
refereed = {yes},
length = {20},
url = {https://drops.dagstuhl.de/opus/volltexte/2020/12352/}
}
[Cerna]

Higher-order pattern generalization modulo equational theories

David M. Cerna, Temur Kutsia

Mathematical Structures in Computer Science 30(6), pp. 627-663. 2020. ISSN 0960-1295. [url]
[bib]
@article{RISC6226,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-order pattern generalization modulo equational theories}},
language = {english},
journal = {Mathematical Structures in Computer Science},
volume = {30},
number = {6},
pages = {627--663},
isbn_issn = {ISSN 0960-1295},
year = {2020},
refereed = {yes},
length = {37},
url = {https://www.cambridge.org/core/services/aop-cambridge-core/content/view/88E26F155F0FD02B3EDD648971D9AD1B/S0960129520000110a.pdf/higher-order-pattern-generalization-modulo-equational-theories.pdf}
}
[Cerna]

Unital Anti-Unification: Type and Algorithms

David M. Cerna , Temur Kutsia

In: 5th International Conference on Formal Structures for Computation and Deduction, {FSCD} 2020, June 29-July 6, 2020, Paris, France (Virtual Conference, Zena M. Ariola (ed.), Proceedings of FSCD, LIPICS 167/20-02, pp. 1-20. 2020. 1868-8969. [doi]
[bib]
@inproceedings{RISC6237,
author = {David M. Cerna and Temur Kutsia},
title = {{Unital Anti-Unification: Type and Algorithms}},
booktitle = {{5th International Conference on Formal Structures for Computation and Deduction, {FSCD} 2020, June 29-July 6, 2020, Paris, France (Virtual Conference}},
language = {english},
abstract = {Unital equational theories are defined by axioms that assert the existence of the unit element for some function symbols. We study anti-unification (AU) in unital theories and address the problems of establishing generalization type and designing anti-unification algorithms. First, we prove that when the term signature contains at least two unital functions, anti-unification is of the nullary type by showing that there exists an AU problem, which does not have a minimal complete set of generalizations. Next, we consider two special cases: the linear variant and the fragment with only one unital symbol, and design AU algorithms for them. The algorithms are terminating, sound, complete and return tree grammars from which set of generalizations can be constructed. Anti-unification for both special cases is finitary. Further, the algorithm for the one-unital fragment is extended to the unrestricted case. It terminates and returns a tree grammar which produces an infinite set of generalizations. At the end, we discuss how the nullary type of unital anti-unification might affect the anti-unification problem in some combined theories, and list some open questions. },
series = {LIPICS},
volume = {167},
number = {20-02},
pages = {1--20},
isbn_issn = {1868-8969},
year = {2020},
editor = {Zena M. Ariola},
refereed = {yes},
keywords = {Anti-unification, tree grammars, unital theories, collapse theories},
length = {19},
conferencename = {FSCD},
url = {https://doi.org/10.4230/LIPIcs.FSCD.2020.26}
}
[Reichl]

The Integration of SMT Solvers into the RISCAL Model Checker

Franz-Xaver Reichl

Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. Master Thesis. April 2020. [pdf]
[bib]
@misc{RISC6103,
author = {Franz-Xaver Reichl},
title = {{The Integration of SMT Solvers into the RISCAL Model Checker}},
language = {english},
abstract = {In this thesis we present an alternative approach to check specifications from asubstantial subset of the RISC Algorithm Language (RISCAL). The main goal forthis new approach is to speed up checks done in RISCAL. For this purpose wedeveloped a translation from the RISCAL language to the SMT-LIB language (usingthe QF_UFBV logic). The realisation of this translation in particular required to solvethe problems of eliminating RISCAL’s quantifiers and of encoding RISCAL’s typesand operations. We formally described core components of this translation, provedsome aspects of their correctness, and implemented it in the programming languageJava. We tested the implementation together with the SMT solvers Boolector, CVC4,Yices and Z3, on several real world RISCAL specifications. Additionally, we evaluatedthe performance of our approach by systematic benchmarks and compared it withthat of the original RISCAL checking mechanism. Finally, we analysed the testsin order to determine patterns in specifications that could possibly have a negativeinfluence on the performance of the presented method. The tests showed that amongthe four used SMT solvers, the solver Yices delivered, for almost all, tests the bestresults. Additionally, the tests indicated that the translation is indeed a viablealternative to RISCAL’s current checking method, especially when used togetherwith Yices. So the translation used with Yices was substantially faster than RISCALin approximately 75% of the test cases. Nevertheless, the tests also illustrated thatRISCAL could still check certain test cases substantially faster. Thus, the translationcannot fully replace RISCAL’s current checking methods.},
year = {2020},
month = {April},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal methods, automated reasoning, model checking, program verification},
sponsor = {Johannes Kepler University, Linz, Institute of Technology(LIT) project LOGTECHEDU.},
length = {151}
}
[Schreiner]

McCarthy-Kleene fuzzy automata and MSO logics

Manfred Droste, Temur Kutsia, George Rahonis, Wolfgang Schreiner

Information and Computation, pp. -. 2020. Elsevier, ISSN 0890-5401. In Press. [doi]
[bib]
@article{RISC6011,
author = {Manfred Droste and Temur Kutsia and George Rahonis and Wolfgang Schreiner},
title = {{McCarthy-Kleene fuzzy automata and MSO logics}},
language = {english},
abstract = {We introduce McCarthy-Kleene fuzzy automata (MK-fuzzy automata) over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages accepted by MK-fuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a Büchi type theorem.},
journal = {Information and Computation},
pages = {--},
publisher = {Elsevier},
isbn_issn = {ISSN 0890-5401},
year = {2020},
note = {In Press},
refereed = {yes},
keywords = {Bimonoids, McCarthy-Kleene logic, MK-fuzzy automata, MK-fuzzy MSO logic},
sponsor = {Supported by the Austrian Research Promotion Agency (FFG) in the frame of the BRIDGE program 846003 “LogicGuard II”},
length = {23},
url = {https://doi.org/10.1016/j.ic.2019.104499}
}
[Schreiner]

The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking

Ádam Tóth, Tamas Bérczes, Janos Sztrik, Attila Kuki, Wolfgang Schreiner

Journal of Mathematical Sciences 246(4), pp. 548-559. March 2020. ISSN 1573-8795. [doi]
[bib]
@article{RISC6088,
author = {Ádam Tóth and Tamas Bérczes and Janos Sztrik and Attila Kuki and Wolfgang Schreiner},
title = {{The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking}},
language = {english},
abstract = {This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.},
journal = {Journal of Mathematical Sciences },
volume = {246},
number = {4},
pages = {548--559},
isbn_issn = {ISSN 1573-8795},
year = {2020},
month = {March},
refereed = {yes},
sponsor = {Austrian-Hungarian Bilateral Cooperation in Science and Tech- nology project 2017-2.2.4-TeT-AT-2017-00010},
length = {12},
url = {https://doi.org/10.1007/s10958-020-04759-4}
}
[Schreiner]

Mathematical Model Checking Based on Semantics and SMT

Wolfgang Schreiner, Franz-Xaver Reichl

Transactions on Internet Research 16(2), pp. 4-13. July 2020. IPSI, ISSN 1820-4503. [url]
[bib]
@article{RISC6117,
author = {Wolfgang Schreiner and Franz-Xaver Reichl},
title = {{Mathematical Model Checking Based on Semantics and SMT}},
language = {english},
abstract = {We report on the usage and implementation of RISCAL, a model checker formathematical theories and algorithms based on a variant of first-order logicwith finite models; this allows to automatically decide the validity of allformulas and to verify the correctness of all algorithms specified by suchformulas. We describe the semantics-based implementation of the checker aswell as a recently developed alternative based on SMT solving, andexperimentally compare their performance. Furthermore, we report on ourexperience with RISCAL for enhancing education in computer science andmathematics, in particular in academic courses on logic, formal methods, andformal modeling. By the use of this software, students are encouraged toactively engage with the course material by solving concrete problems wherethe correctness of a solution is automatically checked; if a solution is notcorrect or the student gets stuck, the software provides additional insightand hints that aid the student towards the desired result.},
journal = {Transactions on Internet Research},
volume = {16},
number = {2},
pages = {4--13},
publisher = {IPSI},
isbn_issn = {ISSN 1820-4503},
year = {2020},
month = {July},
refereed = {yes},
keywords = {model checking, logic, semantics, formal verification, reasoning about programs, computer science education},
sponsor = {Johannes Kepler University, Linz, Institute of Technology(LIT) project LOGTECHEDU and OEAD WTZ project SK 14/2018 SemTech},
length = {10},
url = {http://ipsitransactions.org/journals/papers/tir/2020jul/p2.pdf}
}

2019

[Cerna]

Evaluation of the VL Logic (342.208-9) 2018W End of Semester Questionnaire

David M. Cerna

Submitted to the RISC Report Series. Feburary 2019. [xlsx] [pdf]
[bib]
@techreport{RISC5885,
author = {David M. Cerna},
title = {{Evaluation of the VL Logic (342.208-9) 2018W End of Semester Questionnaire}},
language = {english},
abstract = {In this technical report we cover the choice of layout and intentions behind our end of the semester questionnaire as well as our interpretation of student answers, resulting statistical analysis, and inferences. Our questionnaire is to some extent free-form in that we provide instructions concerning the desired content of the answers but leave the precise formulation of the answer to the student. Our goal, through this approach, was to gain an understanding of how the students viewed there own progress and interest in the course without explicitly guiding them. Towards this end, we chose to have the students draw curves supplemented by short descriptions of important features. We end with a discussion of the benefits and downsides of such a questionnaire as well as what the results entail concerning future iterations of the course. },
year = {2019},
month = {Feburary},
length = {17},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Cerna]

The Castle Game

David M. Cerna

Submitted to the RISC Report Series. 2019. [pdf]
[bib]
@techreport{RISC5886,
author = {David M. Cerna},
title = {{The Castle Game}},
language = {english},
abstract = {A description of a game for teaching certain aspects of first-order logic based on the Drink's Paradox. },
year = {2019},
length = {3},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Cerna]

Manual for AXolotl

David M. Cerna

Submitted to the RISC Report Series. 2019. [zip] [pdf] [jar]
[bib]
@techreport{RISC5887,
author = {David M. Cerna},
title = {{Manual for AXolotl}},
language = {english},
abstract = {In this document we outline how to play our preliminary version of \textbf{AX}olotl. We present a sequence of graphics illustrating the step by step process of playing the game. },
year = {2019},
length = {9},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Cerna]

AXolotl: A Self-study Tool for First-order Logic

David Cerna

Submitted to the RISC Report Series. May 2019. [pdf]
[bib]
@techreport{RISC5936,
author = {David Cerna},
title = {{AXolotl: A Self-study Tool for First-order Logic}},
language = {english},
year = {2019},
month = {May},
length = {4},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Cerna]

A Generic Framework for Higher-Order Generalizations

David M. Cerna, Temur Kutsia

In: Proceedings of the 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019), Herman Geuvers (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 131, pp. 10:1-10:19. 2019. Schloss Dagstuhl, ISSN 1868-8969. [doi]
[bib]
@inproceedings{RISC5947,
author = {David M. Cerna and Temur Kutsia},
title = {{A Generic Framework for Higher-Order Generalizations}},
booktitle = {{Proceedings of the 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {131},
pages = {10:1--10:19},
publisher = {Schloss Dagstuhl},
isbn_issn = {ISSN 1868-8969},
year = {2019},
editor = {Herman Geuvers},
refereed = {yes},
length = {19},
url = {http://dx.doi.org/10.4230/LIPIcs.FSCD.2019.10}
}
[Cerna]

On the Complexity of Unsatisfiable Primitive Recursively defined $\Sigma_1$-Sentences

David M. Cerna

Submitted to the RISC Report Series. 2019. [pdf]
[bib]
@techreport{RISC5981,
author = {David M. Cerna},
title = {{On the Complexity of Unsatisfiable Primitive Recursively defined $\Sigma_1$-Sentences}},
language = {english},
abstract = {We introduce a measure of complexity based on formula occurrence within instance proofs of an inductive statement. Our measure is closely related to {\em Herbrand Sequent length}, but instead of capturing the number of necessary term instantiations, it captures the finite representational difficulty of a recursive sequence of proofs. We restrict ourselves to a class of unsatisfiable primitive recursively defined negation normal form first-order sentences, referred to as {\em abstract sentences}, which capture many problems of interest; for example, variants of the {\em infinitary pigeonhole principle}. This class of sentences has been particularly useful for inductive formal proof analysis and proof transformation. Together our complexity measure and abstract sentences allow use to capture a notion of {\em tractability} for state-of-the-art approaches to inductive theorem proving, in particular {\em loop discovery} and {\em tree grammar} based inductive theorem provers. We provide a complexity analysis of an important abstract sentence, and discuss the analysis of a few related sentences, based on the infinitary pigeonhole principle which we conjecture represent the upper limits of tractability and foundation of intractability with respect to the current approaches.},
year = {2019},
length = {17},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Cerna]

A Mobile Application for Self-Guided Study of Formal Reasoning

David M. Cerna and Rafael Kiesel and Alexandra Dzhiganskaya

Submitted to the RISC Report Series. October 2019. [pdf]
[bib]
@techreport{RISC5991,
author = {David M. Cerna and Rafael Kiesel and Alexandra Dzhiganskaya},
title = {{A Mobile Application for Self-Guided Study of Formal Reasoning}},
language = {english},
abstract = {In this work we introduce AXolotl, a self-study aid designed to guide students through the basics offormal reasoning and term manipulation. Unlike most of the existing study aids for formal reasoning,AXolotl is an Android-based application with a simple touch-based interface. Part of the design goalwas to minimize the possibility of user errors which distract from the learning process. Such as typosor inconsistent application of the provided rules. The system includes a zoomable proof viewer whichdisplays the progress made so far and allows for storage of the completed proofs as a JPEG or L A TEXfile. The software is available on the google play store and comes with a small library of problems.Additional problems may be opened in AXolotl using a simple input language. Currently, AXolotlsupports problems which can be solved using rules which transform a single expression into a set ofexpressions. This covers educational scenarios found in our first semester introduction to logic courseand helps bridge the gap between propositional and first-order reasoning. Future developments willinclude rewrite rules which take a set of expressions and return a set of expressions, as well as aquantified first-order extension.},
year = {2019},
month = {October},
length = {18},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[Schreiner]

On the Probabilistic Model Checking of a Retrial Queueing System with Unreliable Server, Collision, and Constant Time Impatience

Wolfgang Schreiner, János Sztrik

Technical report no. 19-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). July 2019. [pdf]
[bib]
@techreport{RISC5984,
author = {Wolfgang Schreiner and János Sztrik},
title = {{On the Probabilistic Model Checking of a Retrial Queueing System with Unreliable Server, Collision, and Constant Time Impatience}},
language = {english},
abstract = {We report on initial experiments with the automated analysis of a finite-source queueingsystem with an unreliable server and collisions of service requests that cause clients to bemoved to an orbit until they can be served. However, clients remain in the obit only forsome maximum amount of time before they run out of patience and unsuccessfully aborttheir service request. In contrast to earlier investigations, the duration of their patience isnot exponentially distributed but constrained by a constant time bound, which imposes aproblem for both their manual and automatic analysis. In this paper we address how suchsystems can be nevertheless approximately analyzed to a certain extent with the help of theprobabilistic model checker PRISM.},
number = {19-11},
year = {2019},
month = {July},
keywords = {formal methods, model checking, performance analysis},
sponsor = {Supported by the Austrian-Hungarian Bilateral Cooperation in Science and Technology project 2017-2.2.4-TeT- AT-2017-00010 and the Aktion Österreich-Ungarn project 101öu7.},
length = {21},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

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