We show how to obtain stochastic bounds for the strong stochastic ordering and the concave ordering of the maximal flow in a network where the capacities are non negative discrete random variables. While the deterministic problem is polynomial, the stochastic version with discrete random variables is NP-hard. The monotonicity of the Min-Cut problem for these stochastic orderings allows us to simplify the input distributions and obtain bounds on the results. Thus we obtain a tradeoff between the complexity of the computations and the precision of the bounds. We illustrate the approach with some examples.
Algebras can be used to interpret the behaviour of effectful programs. In particular, we use Eilenberg-Moore algebras given over a complete lattices of truth values, which specify answers to queries about programs. The algebras can be used to formulate a quantitative logic of behavioural properties, specifying a congruent notion of program equivalence coinciding with a notion of applicative bisimilarity. Many combinations of effects can be interpreted using these algebras. In this paper, we specify a method of generically combining effects and the algebras used to interpret them. At the core of this method is the tensor of complete lattices, which combines the carrier sets of the algebras. We show that this tensor preserves complete distributivity of complete lattices. Moreover, the universal properties of this tensor can then be used to properly combine the Eilenberg-Moore algebras. We will apply this method to combine the effects of probability, global store, cost, nondeterminism, and error effects. We will then compare this method of combining effects with the more traditional method of combining equational theories using interaction laws.
The analysis of information flow is a popular technique for ensuring the confidentiality of data. It is in this context that confidentiality policies arise for giving guarantees that private data cannot be inferred by the inspection of public data. One of those policies is non-interference, a semantic condition that ensures the absence of illicit information flow during program execution by not allowing to distinguish the results of two computations when they only vary in their confidential inputs. A remarkable feature of non-interference is that it can be enforced statically by the definition of information flow type systems. In those type systems, if a program type-checks, then it means that it meets the security policy. In this paper we focus on the preservation of non-interference through program translation. Concretely, we formalize the proof of security preservation of Hunt and Sands' translation that transforms high-level While programs typable in a flow-sensitive type system into equivalent high-level programs typable in a flow-insensitive type system. Our formalization is performed in the dependently-typed language Agda. We use the expressive power of Agda's type system to encode the security type systems at the type level. A particular aspect of our formalization is that it follows a fully internalist approach where we decorate the type of the abstract syntax with security type information in order to obtain the representation of well-typed (i.e secure) programs. A benefit of this approach is that it allows us to directly express the property of security preservation in the type of the translation relation. In this manner, apart from inherently expressing the transformation of programs, the translation relation also stands for an inductive proof of security preservation.
The bond-calculus is a language for modelling interactions between continuous populations of biomolecular agents. The calculus combines process-algebra descriptions of individual agent behaviour with affinity patterns, which can specify a wide variety of patterns of interactions between the sites of different agents. These affinity patterns extend binary molecular affinities to multiway reactions, general kinetic laws, and cooperative interactions. In this paper we explore bond-calculus modelling of gene regulation at both the molecular and network levels. At the molecular level, we show how affinity patterns can succinctly describe the λ-switch, a prototypical example of cooperative regulation. Moving to the network level, we develop a general model of gene regulatory networks using affinity patterns and an expanded Hill kinetic law. We illustrate the approach with a specific example: the complex plant circadian clock. We analyse these models via the bond-calculus's differential equation and stochastic semantics, and validate our results against existing models from the literature.
In this paper we present a modeling approach suitable for practical evaluation of the delays that may affect security monitoring systems in (multitenant) cloud based architecture, and in general to support professionals in planning and evaluating relevant parameters in dealing with new designs or migration projects. The approach is based on modularity and multiformalism techniques to manage complexity and guide designers in an incremental process, to help transferring technical knowledge into modeling practice and to help easing the use of simulation. We present a case study based on a real experience, triggered by a new legal requirement that Italian Public Administration should comply about their datacenters.
Besides tutoring and consultancies, the development of academic and scientific documents in universities evidenced collaborative work. This paper presents an ontology-based approach to describe different modes of collaboration by reusing and enriching data from an institutional repository, from a collection of posters. The approach uses an application ontology that makes explicit the relationships among authors and posters. The paper presents a list of competency questions that are answered in natural language and by the ontology terminology. The proposed approach is of value as this offers machine-readable data to support further analysis and inference mechanisms. This paper represents a reviewed version of the described for the CEUR proceedings for the "Twelfth Latin American Workshop on New Methods of Reasoning 2019 Logic / Languages, Algorithms, New Methods of Reasoning (LANMR 2019)".
Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained as a partial evaluation of "2+2+1". This construction can be given for any monad, and it is linked to the famous bar construction [15, VII.6], of which it gives an operational interpretation: the bar construction is a simplicial set, and its 1-cells are partial evaluations. We study the properties of partial evaluations for general monads. We prove that whenever the monad is weakly cartesian, partial evaluations can be composed via the usual Kan filler property of simplicial sets, of which we give an interpretation in terms of substitution of terms. For the case of probability monads, partial evaluations correspond to what probabilists call conditional expectation of random variables, and partial evaluation relation is known as second-order stochastic dominance. In terms of rewritings, partial evaluations give an abstract reduction system which is reflexive, confluent, and transitive whenever the monad is weakly cartesian. This manuscript is part of a work in progress on a general rewriting interpretation of the bar construction.
Continuous monads are an axiomatic class of submonads of the double power set monad. ρ-sets are an axiomatic generalization of directed sets. The ρ-generalization of continuous lattices arises as the algebras of a continuous monad and conversely. Each ρ-continuous poset has two topologies which respectively generalize the Scott and Lawson topologies. Each ρ-contnuous lattice is compact in the canonical topology if and only if the corresponding continuous monad contains the ultrafilter monad.
Rational McNaughton functions may be implicitly represented by logical formulas in Łukasiewicz Infinitely-valued Logic by constraining the set of valuations to the ones that satisfy some specific formulas. This work investigates this implicit representation called representation modulo satisfiability and describes a polynomial algorithm that builds it — the representative formula and the constraining ones — for a given rational McNaughton function.
This paper introduces a sort of automata and associated languages, often arising in modelling natural phenomena, in which both vagueness and simultaneity are taken as first class citizens. This requires a fuzzy semantics assigned to transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The expected relationships between automata and languages are revisited in this setting; in particular it is shown that any subset of a fuzzy synchronous language with the suitable signature forms a synchronous Kleene algebra.
A domain-theoretic method for solving initial value problems (IVPs) is presented, together with proofs of soundness, completeness, and some results on the algebraic complexity of the method. While the common fixed-precision interval arithmetic methods are restricted by the precision of the underlying machine architecture, domain-theoretic methods may be complete, i.e., the result may be obtained to any degree of accuracy. Furthermore, unlike methods based on interval arithmetic which require access to the syntactic representation of the vector field, domain-theoretic methods only deal with the semantics of the field, in the sense that the field is assumed to be given via finitely-representable approximations, to within any required accuracy. In contrast to the domain-theoretic first-order Euler method, the second-order method uses the local Lipschitz properties of the field. This is achieved by using a domain for Lipschitz functions, whose elements are consistent pairs that provide approximations of the field and its local Lipschitz properties. In the special case where the field is differentiable, the local Lipschitz properties are exactly the local differential properties of the field. In solving IVPs, Lipschitz continuity of the field is a common assumption, as a sufficient condition for uniqueness of the solution. While the validated methods for solving IVPs commonly impose further restrictions on the vector field, the second-order Euler method requires no further condition. In this sense, the method may be seen as the most general of its kind. To avoid complicated notations and lengthy arguments, the results of the paper are stated for the second-order Euler method. Nonetheless, the framework, and the results, may be extended to any higher-order Euler method, in a straightforward way.
We address the problem of selecting a model from a list of potential models in the field of dynamical systems. The selection is based on model behaviour specified in temporal logic rather than time series. This provides more global constraints on the system dynamics. Not only to select one model but also to create an ordered structure, we propose the model ordering problem. We suggest and apply several ordering relations comparing models given property specification. To provide a formal method with global results for the proposed setting we employ and adapt model checking and parameter synthesis methods. To evaluate the method, we apply the proposed method to several qualitative models of regulatory networks.
In the area of Markovian quantitative modelling, compositional model specification techniques such as Stochastic Process Algebra are widely used. However, exploiting a model's compositional structure for efficient analysis is still a difficult problem and mostly limited to special cases. This paper addresses some important issues in the area of compositional model checking of Markovian models for models with Boucherie-type product form. It closes a long-standing gap concerning the question whether compositional model checking of so-called global time-unbounded Until formulas is possible. The answer to this turns out to be negative. The paper then turns to the area of model repair, i.e. the question of how to fix a model in case it violates a given requirement. Here another general result and a useful proposition for compositional model repair are provided.
In this paper we present two performance models of a web-based sales system, one without the presence of an attack and the other with the presence of a denial of service attack. Models are formulated using the PEPA formalism. The PEPA eclipse plug-in is used to support the creation of the PEPA models for the web-based sales system and the automatic calculation of the performance measures identified to evaluate the models. The evaluation of the models illustrates how the performance of the warehouse's sale is negatively affected by denial of service attack through preventing some or all customers' orders from being fulfilled. The resultant delay on selling perishable products would result on products being discarded.
We present a dual sequent calculus for the necessity fragment of the constructive modal logic S4 and show its adequacy for proof-search in the style of modern interactive theorem provers. The main feature of dual systems is the use of two contexts to capture the notions of true and valid formulas, without using any formal semantics. This attribute allows us to give simple rules for the □ operator that, most of the time, grant the substitution of a strict modal reasoning by a pure propositional one, thus simplifying the proof-search process. Moreover, we introduce a formal notion of backward proof corresponding to a bottom-up construction of a derivation tree by means of a left-to-right depth-first proof-search.
This paper focuses on a major improvement on the analysis of reachability properties in large-scale dynamical biological models. To tackle such models, where classical model checkers fail due to state space explosion led by exhaustive search. Alternative static analysis approaches have been proposed, but they may also fail in certain cases due to non-exhaustive search. In this paper, we introduce a hybrid approach ASPReach, which combines static analysis and stochastic search to break the limits of both approaches. We tackle this issue on a modeling framework we recently introduced, Asynchronous Binary Automata Network (ABAN). We show that ASPReach is able to analyze efficiently some reachability properties which could not be solved by existing methods. We studied also various cases from biological literature, emphasizing the merits of our approach in terms of conclusiveness and performance.
We present a proof of the equivalence between two deductive systems for the constructive modal logic S4. On one side, an axiomatic characterization inspired by Hakli and Negri's Hilbert-style system of derivations from assumptions for modal logic K. On the other side, the judgmental reconstruction given by Pfenning and Davies by means of a so-called dual natural deduction approach that makes a distinction between valid, true and possible formulas. Both systems and the proof of their equivalence are formally verified using the Coq proof assistant.
One of the most fundamental properties of a proof system is analyticity, expressing the fact that a proof of a given formula F only uses subformulas of F. In sequent calculus, this property is usually proved by showing that the cut rule is admissible, i.e., the introduction of the auxiliary lemma A in the reasoning “if A follows from B and C follows from A, then C follows from B” can be eliminated. Mathematically, this means that we can inline the intermediate step A to have a direct proof of C from the hypothesis B. More importantly, the proof of cut-elimination shows that the proof of C follows directly from the axiomatic theory and B (and no external lemmas are needed). The proof of cut-elimination is usually a tedious process through several proof transformations, thus requiring the assistance of (semi-)automatic procedures to avoid mistakes. In a previous work by Miller and Pimentel, linear logic (LL) was used as a logical framework for establishing sufficient conditions for cut-elimination of object logics (OL). The OL's inference rules were encoded as an LL theory and an easy-to-verify criterion sufficed to establish the cut-elimination theorem for the OL at hand. Using such procedure, analyticity of logical systems such as LK (classical logic), LJ (intuitionistic logic) and substructural logics such as MALL (multiplicative additive LL) was proved within the framework. However, there are many logical systems that cannot be adequately encoded in LL, the most symptomatic cases being sequent systems for modal logics. In this paper we use a linear-nested sequent (LNS) presentation of SLL (a variant of linear logic with subexponentials) and show that it is possible to establish a cut-elimination criterion for a larger class of logical systems, including LNS proof systems for K, 4, KT, KD, S4 and the multi-conclusion LNS system for intuitionistic logic (mLJ). Impressively enough, the sufficient conditions for cut-elimination presented here remain as simple as the one proposed by Miller and Pimentel. The key ingredient in our developments is the use of the right formalism: we adopt LNS based OL systems, instead of sequent ones. This not only provides a neat encoding procedure of OLs into SLL, but it also allows for the use of the meta-theory of SLL to establish fundamental meta-properties of the encoded OLs. We thus contribute with procedures for checking cut-elimination of several logical systems that are widely used in philosophy, mathematics and computer science.
The Robust Transform based on the Weighted Median operator algorithm calculates the transform of a signal when it has been exposed to impulsive noise. Since this algorithm demands very long execution time, it is not useful for real time signal processing systems. In this context, this work presents several strategies to improve its performance, such as the reduction of redundant calculations, optimization in the memory access, and a multithreads version of the algorithm. Besides, the original estimation method is modified to decrease even more the average execution time, keeping the quality level of the numeric results. The experimental results show a 30% performance improvement by reducing redundant calculations and optimizing the memory access, without making modifications to the estimation method and without using multi-threaded processing; 93% performance improvement by introducing modifications to the estimation method; and 97% performance improvement by incorporating the multi-threaded processing.
Weakest precondition transformers are useful tools in program verification. One of their key properties is compositionality, that is, the weakest precondition predicate transformer (wppt for short) associated to program f;g should be equal to the composition of the wppts associated to f and g. In this paper, we study the categorical structure behind wppts from a fibrational point of view. We characterize the wppts that satisfy compositionality as the ones constructed from the Cartesian lifting of a monad. We moreover show that Cartesian liftings of monads along lax slice categories bijectively correspond to Eilenberg-Moore monotone algebras. We then instantiate our techniques by deriving wppts for commonplace effects such as the maybe monad, the non-empty powerset monad, the counter monad or the distribution monad. We also show how to combine them to derive the wppts appearing in the literature of verification of probabilistic programs.
