In 1969, Tarski asked whether the arithmetic identities taught in high school are complete for sh... more In 1969, Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. We know the answer to this question for various subsystems obtained by restricting in different ways the language of arithmetic expressions, yet, up to now we knew nothing of the original system that Tarski considered when he started all this research, namely the theory of integers under sum, product, exponentiation with two constants for zero and one. This paper closes this long standing open problem, by providing an elementary proof, relying on previous work of R. Gurevič, of the fact that Tarski’s original system is decidable, yet not finitely aximatisable. We also show some consequences of this result for the theory of isomorphisms of types.
We introduce a semantics of Logic Programming based on an classical Game Theory, which is proven ... more We introduce a semantics of Logic Programming based on an classical Game Theory, which is proven to be sound and complete wrt the traditional operational semantics and Negation as Failure. This game semantics is based on an abstract reformulation of classical results about two player games, and allows a very simple characterization of the solution set of a logic program in terms of approximations of the value of the game associated to it, which can also be used to capture in a very simple way the traditional “negation as failure” ...
ABSTRACT We introduce the Aeolus component model, which is specifically designed to capture reali... more ABSTRACT We introduce the Aeolus component model, which is specifically designed to capture realistic scenarii arising when configuring and deploying distributed applications in the so-called cloud environments, where interconnected components can be deployed on clusters of heterogeneous virtual machines, which can be in turn created, destroyed, and connected on-the-fly.The full Aeolus model is able to describe several component characteristics such as dependencies, conflicts, non-functional requirements (replication requests and load limits), as well as the fact that component interfaces to the world might vary depending on the internal component state.When the number of components needed to build an application grows, it becomes important to be able to automate activities such as deployment and reconfiguration. This correspond, at the level of the model, to the ability to decide whether a desired target system configuration is reachable, which we call the achievability problem, and producing a path to reach it.In this work we show that the achievability problem is undecidable for the full Aeolus model, a strong limiting result for automated configuration in the cloud. We also show that the problem becomes decidable, but Ackermann-hard, as soon as one drops non-functional requirements. Finally, we provide a polynomial time algorithm for the further restriction of the model where support for inter-component conflicts is also removed.
Abstract In this paper, we show the correspondence existing between normalization in calculi with... more Abstract In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for linear logic, via proof nets. This correspondence allows us to prove that a typed version of the λx-calculus is strongly normalizing, as well as of all the calculi that can be translated to it keeping normalization properties such as λ v, λ s, λ d and λ f. In order to achieve this result, we introduce a new notion of reduction in proof nets: this extended reduction is still confluent ...
Symposium on Programming Language Implementation and Logic Programming, 1996
This work focuses on software reuse for languages equipped with a module system. To retrieve modu... more This work focuses on software reuse for languages equipped with a module system. To retrieve modules from a library, it is quite reasonable to use module signatures as a search key, up to a suitable notion of signature isomorphism.
A wealth of protocols for electronic voting have been proposed in the literature over the past ye... more A wealth of protocols for electronic voting have been proposed in the literature over the past years. What makes these protocols diffi- cult to conceive and verify is one fundamental property, anonymity, which is of paramount importance in the real world, in particular when performing actual political elections. Historically, certain techniques have been used in actual elections to nullify anonymity and effectively coerce voters, by exploiting an evident weakness in many voting protocols; these techniques were used in traditional elections well before the notion of electronic vot- ing was even proposed, yet, they still seem to be little known: as a consequence, we find recent proposals of voting protocols that can easily be attacked this way, like (Riv06), or clever attempts at for- mal definitions of privacy and anonymity properties that would not rule out such flawed protocols, like (DKR06). In this paper, we describe one old technique, effectively used in Italy over twenty years ...
Información del artículo Proof nets and explicit substitutions Using various translations of the ... more Información del artículo Proof nets and explicit substitutions Using various translations of the $\l$-calculus into proof nets, new abstract machines have been proposed that exploit the Geometry of Interaction and Dynamic Algebras (Girard 1989; Abramsky and Jagadeesan 1992; Danos 1990), leading to work on optimal reduction (Gonthier et al. 1992; Lamping 1990).
Abstract This paper provides a formal treatment of isomorphic types for languages equipped with a... more Abstract This paper provides a formal treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. The results obtained make less justified the commonplace feeling that (the core of) ML is a subset of second order X-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order A-calculus. This new isomorphism allows to provide a complete (and decidable) axiomatization of all the types isomorphic in ML style languages, a relevant ...
In 1969, Tarski asked whether the arithmetic identities taught in high school are complete for sh... more In 1969, Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. We know the answer to this question for various subsystems obtained by restricting in different ways the language of arithmetic expressions, yet, up to now we knew nothing of the original system that Tarski considered when he started all this research, namely the theory of integers under sum, product, exponentiation with two constants for zero and one. This paper closes this long standing open problem, by providing an elementary proof, relying on previous work of R. Gurevič, of the fact that Tarski’s original system is decidable, yet not finitely aximatisable. We also show some consequences of this result for the theory of isomorphisms of types.
We introduce a semantics of Logic Programming based on an classical Game Theory, which is proven ... more We introduce a semantics of Logic Programming based on an classical Game Theory, which is proven to be sound and complete wrt the traditional operational semantics and Negation as Failure. This game semantics is based on an abstract reformulation of classical results about two player games, and allows a very simple characterization of the solution set of a logic program in terms of approximations of the value of the game associated to it, which can also be used to capture in a very simple way the traditional “negation as failure” ...
ABSTRACT We introduce the Aeolus component model, which is specifically designed to capture reali... more ABSTRACT We introduce the Aeolus component model, which is specifically designed to capture realistic scenarii arising when configuring and deploying distributed applications in the so-called cloud environments, where interconnected components can be deployed on clusters of heterogeneous virtual machines, which can be in turn created, destroyed, and connected on-the-fly.The full Aeolus model is able to describe several component characteristics such as dependencies, conflicts, non-functional requirements (replication requests and load limits), as well as the fact that component interfaces to the world might vary depending on the internal component state.When the number of components needed to build an application grows, it becomes important to be able to automate activities such as deployment and reconfiguration. This correspond, at the level of the model, to the ability to decide whether a desired target system configuration is reachable, which we call the achievability problem, and producing a path to reach it.In this work we show that the achievability problem is undecidable for the full Aeolus model, a strong limiting result for automated configuration in the cloud. We also show that the problem becomes decidable, but Ackermann-hard, as soon as one drops non-functional requirements. Finally, we provide a polynomial time algorithm for the further restriction of the model where support for inter-component conflicts is also removed.
Abstract In this paper, we show the correspondence existing between normalization in calculi with... more Abstract In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for linear logic, via proof nets. This correspondence allows us to prove that a typed version of the λx-calculus is strongly normalizing, as well as of all the calculi that can be translated to it keeping normalization properties such as λ v, λ s, λ d and λ f. In order to achieve this result, we introduce a new notion of reduction in proof nets: this extended reduction is still confluent ...
Symposium on Programming Language Implementation and Logic Programming, 1996
This work focuses on software reuse for languages equipped with a module system. To retrieve modu... more This work focuses on software reuse for languages equipped with a module system. To retrieve modules from a library, it is quite reasonable to use module signatures as a search key, up to a suitable notion of signature isomorphism.
A wealth of protocols for electronic voting have been proposed in the literature over the past ye... more A wealth of protocols for electronic voting have been proposed in the literature over the past years. What makes these protocols diffi- cult to conceive and verify is one fundamental property, anonymity, which is of paramount importance in the real world, in particular when performing actual political elections. Historically, certain techniques have been used in actual elections to nullify anonymity and effectively coerce voters, by exploiting an evident weakness in many voting protocols; these techniques were used in traditional elections well before the notion of electronic vot- ing was even proposed, yet, they still seem to be little known: as a consequence, we find recent proposals of voting protocols that can easily be attacked this way, like (Riv06), or clever attempts at for- mal definitions of privacy and anonymity properties that would not rule out such flawed protocols, like (DKR06). In this paper, we describe one old technique, effectively used in Italy over twenty years ...
Información del artículo Proof nets and explicit substitutions Using various translations of the ... more Información del artículo Proof nets and explicit substitutions Using various translations of the $\l$-calculus into proof nets, new abstract machines have been proposed that exploit the Geometry of Interaction and Dynamic Algebras (Girard 1989; Abramsky and Jagadeesan 1992; Danos 1990), leading to work on optimal reduction (Gonthier et al. 1992; Lamping 1990).
Abstract This paper provides a formal treatment of isomorphic types for languages equipped with a... more Abstract This paper provides a formal treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. The results obtained make less justified the commonplace feeling that (the core of) ML is a subset of second order X-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order A-calculus. This new isomorphism allows to provide a complete (and decidable) axiomatization of all the types isomorphic in ML style languages, a relevant ...
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Papers by Roberto Di Cosmo