Proof Tactics for Theorem Proving Graph Grammars through Rodin

Graph grammar is a formal language suitable for the specification of distributed and concurrent systems. Theorem proving is a technique that allows the verification of systems with huge (and infinite) state space. One of the disadvantages of theorem proving graph grammars (and theorem proving in general) is the specific mathematical knowledge required from the user for concluding the proofs. Previous works have proposed proof strategies to help the developer in the verification process when adopting such approach, firstly establishing proof tactics for some properties and after proposing a visual representation for them. This paper extends the set of proposed tactics, with the aim of expanding the available strategies and encouraging the use of such a technique

Evaluating reasoning heuristics for a hybrid theorem proving platform

Text in English with abstracts in English, Afrikaans and isiZuluThe formalisation of first-order logic and axiomatic set theory in the first half of the 20th century—along with the advent of the digital computer—paved the way for the development of automated theorem proving. In the 1950s, the automation of proof developed from proving elementary geometric problems and finding direct proofs for problems in Principia Mathematica by means of simple, human-oriented rules of inference. A major advance in the field of automated theorem proving occurred in 1965, with the formulation of the resolution inference mechanism. Today, powerful Satisfiability Modulo Theories (SMT) provers combine SAT solvers with sophisticated knowledge from various problem domains to prove increasingly complex theorems. The combinatorial explosion of the search space is viewed as one of the major challenges to progress in the field of automated theorem proving. Pioneers from the 1950s and 1960s have already identified the need for heuristics to guide the proof search effort. Despite theoretical advances in automated reasoning and technological advances in computing, the size of the search space remains problematic when increasingly complex proofs are attempted. Today, heuristics are still useful and necessary to discharge complex proof obligations. In 2000, a number of heuristics was developed to aid the resolution-based prover OTTER in finding proofs for set-theoretic problems. The applicability of these heuristics to next-generation theorem provers were evaluated in 2009. The provers Vampire and Gandalf required respectively 90% and 80% of the applicable OTTER heuristics. This dissertation investigates the applicability of the OTTER heuristics to theorem proving in the hybrid theorem proving environment Rodin—a system modelling tool suite for the Event-B formal method. We show that only 2 of the 10 applicable OTTER heuristics were useful when discharging proof obligations in Rodin. Even though we argue that the OTTER heuristics were largely ineffective when applied to Rodin proofs, heuristics were still needed when proof obligations could not be discharged automatically. Therefore, we propose a number of our own heuristics targeted at theorem proving in the Rodin tool suite.Die formalisering van eerste-orde-logika en aksiomatiese versamelingsteorie in die eerste helfte van die 20ste eeu, tesame met die koms van die digitale rekenaar, het die weg vir die ontwikkeling van geoutomatiseerde bewysvoering gebaan. Die outomatisering van bewysvoering het in die 1950’s ontwikkel vanuit die bewys van elementêre meetkundige probleme en die opspoor van direkte bewyse vir probleme in Principia Mathematica deur middel van eenvoudige, mensgerigte inferensiereëls. Vooruitgang is in 1965 op die gebied van geoutomatiseerde bewysvoering gemaak toe die resolusie-inferensie-meganisme geformuleer is. Deesdae kombineer kragtige Satisfiability Modulo Theories (SMT) bewysvoerders SAT-oplossers met gesofistikeerde kennis vanuit verskeie probleemdomeine om steeds meer komplekse stellings te bewys. Die kombinatoriese ontploffing van die soekruimte kan beskou word as een van die grootste uitdagings vir verdere vooruitgang in die veld van geoutomatiseerde bewysvoering. Baanbrekers uit die 1950’s en 1960’s het reeds bepaal dat daar ’n behoefte is aan heuristieke om die soektog na bewyse te rig. Ten spyte van die teoretiese vooruitgang in outomatiese bewysvoering en die tegnologiese vooruitgang in die rekenaarbedryf, is die grootte van die soekruimte steeds problematies wanneer toenemend komplekse bewyse aangepak word. Teenswoordig is heuristieke steeds nuttig en noodsaaklik om komplekse bewysverpligtinge uit te voer. In 2000 is ’n aantal heuristieke ontwikkel om die resolusie-gebaseerde bewysvoerder OTTER te help om bewyse vir versamelingsteoretiese probleme te vind. Die toepaslikheid van hierdie heuristieke vir die volgende generasie bewysvoerders is in 2009 geëvalueer. Die bewysvoerders Vampire en Gandalf het onderskeidelik 90% en 80% van die toepaslike OTTER-heuristieke nodig gehad. Hierdie verhandeling ondersoek die toepaslikheid van die OTTER-heuristieke op bewysvoering in die hibriede bewysvoeringsomgewing Rodin—’n stelselmodelleringsuite vir die formele Event-B-metode. Ons toon dat slegs 2 van die 10 toepaslike OTTER-heuristieke van nut was vir die uitvoering van bewysverpligtinge in Rodin. Ons voer aan dat die OTTER-heuristieke grotendeels ondoeltreffend was toe dit op Rodin-bewyse toegepas is. Desnieteenstaande is heuristieke steeds nodig as bewysverpligtinge nie outomaties uitgevoer kon word nie. Daarom stel ons ’n aantal van ons eie heuristieke voor wat in die Rodin-suite aangewend kan word.Ukwenziwa semthethweni kwe-first-order logic kanye ne-axiomatic set theory ngesigamu sokuqala sekhulunyaka lama-20—kanye nokufika kwekhompyutha esebenza ngobuxhakaxhaka bedijithali—kwavula indlela ebheke ekuthuthukisweni kwenqubo-kusebenza yokufakazela amathiyoremu ngekhomyutha. Ngeminyaka yawo-1950, ukuqinisekiswa kobufakazi kwasuselwa ekufakazelweni kwezinkinga zejiyomethri eziyisisekelo kanye nasekutholakaleni kobufakazi-ngqo bezinkinga eziphathelene ne-Principia Mathematica ngokuthi kusetshenziswe imithetho yokuqagula-sakucabangela elula, egxile kubantu. Impumelelo enkulu emkhakheni wokufakazela amathiyoremu ngekhompyutha yenzeka ngowe-1965, ngokwenziwa semthethweni kwe-resolution inference mechanism. Namuhla, abafakazeli abanohlonze bamathiyori abizwa nge-Satisfiability Modulo Theories (SMT) bahlanganisa ama-SAT solvers nolwazi lobungcweti oluvela kwizizinda zezinkinga ezihlukahlukene ukuze bakwazi ukufakazela amathiyoremu okungelula neze ukuwafakazela. Ukukhula ngesivinini kobunzima nobunkimbinkimbi benkinga esizindeni esithile kubonwa njengenye yezinselelo ezinkulu okudingeka ukuthi zixazululwe ukuze kube nenqubekela phambili ekufakazelweni kwamathiyoremu ngekhompyutha. Amavulandlela eminyaka yawo-1950 nawo-1960 asesihlonzile kakade isidingo sokuthi amahuristikhi (heuristics) kube yiwona ahola umzamo wokuthola ubufakazi. Nakuba ikhona impumelelo esiyenziwe kumathiyori ezokucabangela okujulile kusetshenziswa amakhompyutha kanye nempumelelo yobuchwepheshe bamakhompyutha, usayizi wesizinda usalokhu uyinkinga uma kwenziwa imizamo yokuthola ubufakazi obuyinkimbinkimbi futhi obunobunzima obukhudlwana. Namuhla imbala, amahuristikhi asewuziso futhi ayadingeka ekufezekiseni izibopho zobufakazi obuyinkimbinkimbi. Ngowezi-2000, kwathuthukiswa amahuristikhi amaningana impela ukuze kulekelelwe uhlelo-kusebenza olungumfakazeli osekelwe phezu kwesixazululo, olubizwa nge-OTTER, ekutholeni ubufakazi bama-set-theoretic problems. Ukusebenziseka kwalawa mahuristikhi kwizinhlelo-kusebenza ezingabafakazeli bamathiyoremu besimanjemanje kwahlolwa ngowezi-2009. Uhlelo-kusebenza olungumfakazeli, olubizwa nge-Vampire kanye nalolo olubizwa nge-Gandalf zadinga ama-90% kanye nama-80%, ngokulandelana kwazo, maqondana nama-OTTER heuristics afanelekile. Lolu cwaningo luphenya futhi lucubungule ukusebenziseka kwama-OTTER heuristics ekufakazelweni kwamathiyoremu esimweni esiyinhlanganisela sokufakazela amathiyoremu esibizwa nge-Rodin—okuyi-system modelling tool suite eqondene ne-Event-B formal method. Kulolu cwaningo siyabonisa ukuthi mabili kuphela kwayi-10 ama-OTTER heuristics aba wusizo ngenkathi kufezekiswa isibopho sobufakazi ku-Rodin. Nakuba sibeka umbono wokuthi esikhathini esiningi ama-OTTER heuristics awazange abe wusizo uma esetshenziswa kuma-Rodin proofs, amahuristikhi asadingeka ezimweni lapho izibopho zobufakazi zingazenzekelanga ngokwazo ngokulawulwa yizinhlelo-kusebenza zekhompyutha. Ngakho-ke, siphakamisa amahuristikhi ethu amaningana angasetshenziswa ekufakazeleni amathiyoremu ku-Rodin tool suite.School of ComputingM. Sc. (Computer Science

Design components

PhD ThesisAlthough it is generally recognised that formal modelling is crucial for ensuring the correctness of software systems, some obstacles to its wider adoption in software engineering persist. One of these is that its productivity is low; another that for modelling techniques and tools to be used efficiently, a broad range of specific skills is required. With the gap between computer performance and engineers’ productivity growing, there is a need to raise the level of abstraction at which development is carried out and off-load much of the routine work done manually today to computers. Formal modelling has all the characteristics required to replace programming and offer higher productivity. Nonetheless, as a branch of software engineering it has yet to be generally accepted. While there is substantial research accumulated in systems analysis and verification, notmuch has been done to foster higher productivity and efficiency of modelling activity. This study puts forward an approach that allows the modeller to encapsulate design ideas and experience in a reusable package. This package, called a design component, can be used in differentways. While a design component is generally intended for constructing a new design using an existing one, we base our approach on a refinement technique. The design encapsulated in the design component is injected into a formal development by formally refining an abstract model. This process is completely automated: the design component is integrated by a tool, with the corresponding correctness proofs also handled automatically. To help us construct design components we consider a number of techniques of transforming models and describing reusable designs. We then introduce the concept ofmodel transformation to encapsulate syntactic rewrite rules used to produce new models. To capture high-level design we introduce the pattern language allowing us to build abstraction and refinement patterns from model transformations. Patterns automate the formal development process and reduce the number of proofs. To help the modeller plan and execute refinement steps, we introduce the concept of themodelling pattern. A modelling pattern combines refinement (or abstraction) patterns with modelling guidelines to form a complete design component

Design components

Although it is generally recognised that formal modelling is crucial for ensuring the correctness of software systems, some obstacles to its wider adoption in software engineering persist. One of these is that its productivity is low; another that for modelling techniques and tools to be used efficiently, a broad range of specific skills is required. With the gap between computer performance and engineers’ productivity growing, there is a need to raise the level of abstraction at which development is carried out and off-load much of the routine work done manually today to computers. Formal modelling has all the characteristics required to replace programming and offer higher productivity. Nonetheless, as a branch of software engineering it has yet to be generally accepted. While there is substantial research accumulated in systems analysis and verification, notmuch has been done to foster higher productivity and efficiency of modelling activity. This study puts forward an approach that allows the modeller to encapsulate design ideas and experience in a reusable package. This package, called a design component, can be used in differentways. While a design component is generally intended for constructing a new design using an existing one, we base our approach on a refinement technique. The design encapsulated in the design component is injected into a formal development by formally refining an abstract model. This process is completely automated: the design component is integrated by a tool, with the corresponding correctness proofs also handled automatically. To help us construct design components we consider a number of techniques of transforming models and describing reusable designs. We then introduce the concept ofmodel transformation to encapsulate syntactic rewrite rules used to produce new models. To capture high-level design we introduce the pattern language allowing us to build abstraction and refinement patterns from model transformations. Patterns automate the formal development process and reduce the number of proofs. To help the modeller plan and execute refinement steps, we introduce the concept of themodelling pattern. A modelling pattern combines refinement (or abstraction) patterns with modelling guidelines to form a complete design component.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Predicting SMT solver performance for software verification

The approach Why3 takes to interfacing with a wide variety of interactive and automatic theorem provers works well: it is designed to overcome limitations on what can be proved by a system which relies on a single tightly-integrated solver. In common with other systems, however, the degree to which proof obligations (or “goals”) are proved depends as much on the SMT solver as the properties of the goal itself. In this work, we present a method to use syntactic analysis to characterise goals and predict the most appropriate solver via machine-learning techniques. Combining solvers in this way - a portfolio-solving approach - maximises the number of goals which can be proved. The driver-based architecture of Why3 presents a unique opportunity to use a portfolio of SMT solvers for software verification. The intelligent scheduling of solvers minimises the time it takes to prove these goals by avoiding solvers which return Timeout and Unknown responses. We assess the suitability of a number of machinelearning algorithms for this scheduling task. The performance of our tool Where4 is evaluated on a dataset of proof obligations. We compare Where4 to a range of SMT solvers and theoretical scheduling strategies. We find that Where4 can out-perform individual solvers by proving a greater number of goals in a shorter average time. Furthermore, Where4 can integrate into a Why3 user’s normal workflow - simplifying and automating the non-expert use of SMT solvers for software verification

Predicting SMT solver performance for software verification

The approach Why3 takes to interfacing with a wide variety of interactive and automatic theorem provers works well: it is designed to overcome limitations on what can be proved by a system which relies on a single tightly-integrated solver. In common with other systems, however, the degree to which proof obligations (or “goals”) are proved depends as much on the SMT solver as the properties of the goal itself. In this work, we present a method to use syntactic analysis to characterise goals and predict the most appropriate solver via machine-learning techniques. Combining solvers in this way - a portfolio-solving approach - maximises the number of goals which can be proved. The driver-based architecture of Why3 presents a unique opportunity to use a portfolio of SMT solvers for software verification. The intelligent scheduling of solvers minimises the time it takes to prove these goals by avoiding solvers which return Timeout and Unknown responses. We assess the suitability of a number of machinelearning algorithms for this scheduling task. The performance of our tool Where4 is evaluated on a dataset of proof obligations. We compare Where4 to a range of SMT solvers and theoretical scheduling strategies. We find that Where4 can out-perform individual solvers by proving a greater number of goals in a shorter average time. Furthermore, Where4 can integrate into a Why3 user’s normal workflow - simplifying and automating the non-expert use of SMT solvers for software verification

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Turku Centre for Computer Science – Annual Report 2013

Due to a major reform of organization and responsibilities of TUCS, its role, activities, and even structures have been under reconsideration in 2013. The traditional pillar of collaboration at TUCS, doctoral training, was reorganized due to changes at both universities according to the renewed national system for doctoral education. Computer Science and Engineering and Information Systems Science are now accompanied by Mathematics and Statistics in newly established doctoral programs at both University of Turku and &Aring;bo Akademi University. Moreover, both universities granted sufficient resources to their respective programmes for doctoral training in these fields, so that joint activities at TUCS can continue. The outcome of this reorganization has the potential of proving out to be a success in terms of scientific profile as well as the quality and quantity of scientific and educational results.&nbsp; International activities that have been characteristic to TUCS since its inception continue strong. TUCS&rsquo; participation in European collaboration through EIT ICT Labs Master&rsquo;s and Doctoral School is now more active than ever. The new double degree programs at MSc and PhD level between University of Turku and Fudan University in Shaghai, P.R.China were succesfully set up and are&nbsp; now running for their first year. The joint students will add to the already international athmosphere of the ICT House.&nbsp; The four new thematic reseach programmes set up acccording to the decision by the TUCS Board have now established themselves, and a number of events and other activities saw the light in 2013. The TUCS Distinguished Lecture Series managed to gather a large audience with its several prominent speakers. The development of these and other research centre activities continue, and&nbsp; new practices and structures will be initiated to support the tradition of close academic collaboration.&nbsp; The TUCS&rsquo; slogan Where Academic Tradition Meets the Exciting Future has proven true throughout these changes. Despite of the dark clouds on the national and European economic sky, science and higher education in the field have managed to retain all the key ingredients for success. Indeed, the future of ICT and Mathematics in Turku seems exciting.</p

Formal analysis of confidentiality conditions related to data leakage

The size of the financial risk, the social repercussions and the legal ramifications resulting from data leakage are of great concern. Some experts believe that poor system designs are to blame. The goal of this thesis is to use applied formal methods to verify that data leakage related confidentiality properties of system designs are satisfied. This thesis presents a practically applicable approach for using Banks's confidentiality framework, instantiated using the Circus notation. The thesis proposes a tool-chain for mechanizing the application of the framework and includes a custom tool and the Isabelle theorem prover that coordinate to verify a given system model. The practical applicability of the mechanization was evaluated by analysing a number of hand-crafted systems having literature related confidentiality requirements. Without any reliable tool for using BCF or any Circus tool that can be extended for the same purpose, it was necessary to build a custom tool. Further, a lack of literature related descriptive case studies on confidentiality in systems compelled us to use hand-written system specifications with literature related confidentiality requirements. The results of this study show that the tool-chain proposed in this thesis is practically applicable in terms of time required. Further, the efficiency of the proposed tool-chain has been shown by comparing the time taken for analysing a system both using the mechanised approach as well as the manual approach