Model checking is an automatic formal verification technique for establishing correctness of systems. It has been widely used in industry for analysing and verifying complex safety-critical systems in application domains such as avionics, medicine and computer security, where manual testing is infeasible and even minor errors could have dire consequences. In our increasingly parallelised world, concurrency has become pivotal and seamlessly woven within programming paradigms, however, extremely challenging when it comes to modelling and establishing correctness of intended behaviour. Tools for model checking concurrent systems face severe limitations due to scalability problems arising from the need to examine all possible interleavings (schedules) of executions of parallel components. Moreover, concurrency poses additional challenges to model checking, giving rise to phenomena such as nondeterminism, deadlock, livelock, etc. In this thesis we focus on adapting and developing novel model-checking techniques for concurrent systems in the setting of the process algebra CSP and its primary model checker FDR. CSP allows for a compact modelling and precise analysis of event-based concurrency, grounded on synchronous message passing as a fundamental mechanism of inter-component communication. In particular, we investigate techniques based on symbolic model checking, static analysis and abstraction, all of them exploiting the compositionality inherent in CSP and targeting to increase the scale of systems that can be tractably analysed. Firstly, we investigate symbolic model-checking techniques based on Boolean satisfiability (SAT), which we adapt for the traces model of CSP. We tailor bounded model checking (BMC), that can be used for bug detection, and temporal k-induction, which aims at establishing inductiveness of properties and is capable of both bug finding and establishing the correctness of systems. Secondly, we propose a static analysis framework for establishing livelock freedom of CSP processes, with lessons for other concurrent formalisms. As opposed to traditional exhaustive state-space exploration, our framework employs a system of rules on the syntax of a process to calculate a sound approximation of its fair/co-fair sets of events. The rules either safely classify a process as livelock-free or report inconclusiveness, thereby trading accuracy for speed. Finally, we develop a series of abstraction/refinement schemes for the traces, stable-failures and failures-divergences models of CSP and embed them into a fully automated and compositional CEGAR framework. For each of those techniques we present an implementation and an experimental evaluation on a set of CSP benchmarks.

Orientador: Itala Maria Loffredo D'Ottaviano / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-09-11T21:14:41Z (GMT). No. of bitstreams: 1 Bueno-Soler_Juliana_D.pdf: 1230879 bytes, checksum: c04ce9e8061c154854f6283749f9c12b (MD5) Previous issue date: 2009 / Resumo: O presente trabalho tem por objetivo investigar o papel da negação no âmbito das modalidades, de forma a poder esclarecer até que ponto a negação pode ser atenuada, controlada ou mesmo totalmente eliminada em favor da melhor expressabilidade lógica de certas teorias, asserções ou raciocínios que sofrem os efeitos da negação. Contudo, atenuar ou eliminar a negação tem um alto preço: métodos tradicionais em lógica podem deixar de ser válidos e certos resultados, como teoremas de completude para sistemas lógicos, podem ser derrogados. Do ponto de vista formal, a questão central que investigamos aqui e até que ponto tais métodos podem ser restabelecidos. Com tal finalidade, iniciamos nosso estudo a partir do que denominamos sistemas anódicos" (sem negação) e, a posteriori, introduzimos gradativamente o elemento catódico" (negações, com diversas gradações e diferentes características) nos sistemas modais por meio de combinações com certas lógicas paraconsistentes, as chamadas lógicas da inconsistência formal (LFIs). Todos os sistemas tratados são semanticamente caracterizados por semânticas de mundos possíveis; resultados de incompletude são também obtidos e discutidos. Obtemos ainda semânticas modais de traduções possíveis para diversos desses sistemas. Avançamos na direção das multimodalidades, investigando os assim chamados sistemas multimodais anódicos e catódicos. Finalmente, procuramos avaliar criticamente o alcance e o interesse dos resultados obtidos na direção da racionalidade sensível à negação. / Abstract: The present work aims to investigate the role of negations in the scope of modalities and in the reasoning expressed by modalities. The investigation starts from what we call anodic" systems (without any form of negation) and gradually reaches the cathodic" elements, where negations are introduced by means of combining modal logics with certain paraconsistent logics known as logics of formal inconsistency (LFIs). We obtain completeness results for all treated systems, and also show that certain incompleteness results can be obtained. The class of the investigated systems includes all normal modal logics that are extended by means of the schema Gk;l;m;n due to E. J. Lemmon and D. Scott combined with LFIs. We also tackle the question of obtaining modal possible-translations semantics for these systems. Analogous results are analyzed in the scope of multimodalities, where anodic as much as cathodic logics are studied. Finally, we advance a critical evaluation of the reach and scope of all the results obtained to what concerns expressibility of reasoning considered to be sensible to negation. We also critically assess the obtained results in contrast with problems of rationality that are sensible to negation. / Doutorado / Doutor em Filosofia

<p>This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D. </p><p>In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains. </p><p>In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained. </p><p>In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations. </p><p>In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.</p>

This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D. In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains. In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained. In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations. In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.

This thesis explores the significance of Godel's Theorem for an understanding of law as rules, and of legal adjudication as rule-following. It argues that Godel's Theorem, read through Wittgenstein's understanding of rules and language as a contextual activity, and through Derrida's account of 'undecidability,' offers an alternative account of the relationship of judging to justice. Instead of providing support for the 'indeterminacy' claim, Godel's Theorem illuminates the predicament of undecidability that structures any interpretation and every legal decision, and which constitutes the opening to justice. The first argument in this thesis examines Godel's proof, Wittgenstein's views on rules, and Derrida's undecidability, as manifestations of a common concern with the limits of what can be formalized. The meta-argument examines their misinterpretation and misappropriation within legal theory as a case study of just what they mean about meaning, context, and justice as necessarily co-implicated.

This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to use this characterization to prove further results about these groups; in particular, results related to the decidability of their universal theories. The latter part of this work consists of a number of independent but related topics. We show that if G is a finitely generated abelian-by-metanilpotent group and H is elementarily equivalent to G then the subgroups gamma_n(G) and gamma_n(H) are elementarily equivalent, as are the quotient groups G/gamma_n(G) and G/gamma_n(H). We go on to consider those groups universally equivalent to F_2(VN_c), where the free groups of the variety V are residually finite p-groups for infinitely many primes p, distinguishing between the cases when c = 1 and when c > 2. Finally, we address some important questions concerning the theories of free groups in product varieties V_k · · ·V_1, where V_i is a nilpotent variety whose free groups are torsion-free; in particular we address questions about the decidability of the elementary and universal theories of such groups. Results mentioned in both of the previous two paragraphs have applications here.

This thesis investigates a method for tackling the verification of parametric systems, systems whose behaviour may depend on the value of one or more parameters. The range of allowable values for such parameters may, in general, be large or unknown. This results in a large number of instances of a system that require verification, one instance for each allowable combination of parameter values. When one or more parameters are unbounded, the family of systems that require verification becomes infinite. Computer protocols are one example of such parametric systems. They may have parameters such as the maximum sequence number or the maximum number of retransmissions. Traditional protocol verification approaches usually only analyse and verify properties of a parametric system for a small range of parameter values. It is impossible to verify in this way every concrete instance of an infinite family of systems. Also, the number of reachable states tends to increase dramatically with increasing parameter values, and thus the well known state explosion phenomenon also limits the range of parameters for which the system can be analysed. In this thesis, we concentrate on the parametric verification of the Stop-and-Wait Protocol (SWP), an elementary flow control protocol. We have used Coloured Petri Nets (CPNs) to model the SWP, operating over an in-order but lossy medium, with two unbounded parameters: the maximum sequence number; and the maximum number of retransmissions. A novel method has been used for symbolically representing the parametric reachability graph of our parametric SWP CPN model. This parametric reachability graph captures exactly the infinite family of reachability graphs resulting from the infinite family of SWP CPNs. The parametric reachability graph is represented symbolically as a set of closed-form algebraic expressions for the nodes and arcs of the reachability graph, expressed in terms of the two parameters. By analysing the reachability graphs of the SWP CPN model for small parameter values, structural regularities in the reachability graphs were identified and exploited to develop the appropriate algebraic expressions for the parametric reachability graph. These expressions can be analysed and manipulated directly, thus the properties that are verified from these expressions are verified for all instances of the system. Several properties of the SWP that are able to be verified directly from the parametric reachability graph have been identified. These include a proof of the size of the parametric reachability graph in terms of both parameters, absence of deadlocks (undesired terminal states), absence of livelocks (undesirable cycles of behaviour from which the protocol cannot escape), absence of dead transitions (actions that can never occur) and the upper bounds on the content of the underlying communication channel. These are verified from the algebraic expressions and thus hold for all parameter values. Significantly, language analysis is also carried out on the parametric SWP. The parametric reachability graph is translated into a parametric Finite State Automaton (FSA), capturing symbolically the infinite set of protocol languages (i.e. sequences of user observable events) by means of similar algebraic expressions to those of the parametric reachability graph. Standard FSA reduction techniques were applied in a symbolic fashion directly to the parametric FSA, firstly to obtain a deterministic representation of the parametric FSA, then to obtain an equivalent minimised FSA. It was found that the determinisation procedure removed the effect of the maximum number of retransmissions parameter, and the minimisation procedure removed the effect of the maximum sequence number parameter. Conformance of all instances of the SWP over both parameters to its desired service language is proved. The development of algebraic expressions to represent the infinite class of Stop-and-Wait Protocols, and the verification of properties (including language analysis) directly from these algebraic expressions, has demonstrated the potential of this method for the verification of more general parametric systems. This thesis provides a significant contribution toward the development of a general parametric verification methodology.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.