318 research outputs found
Multiplicative-Additive Proof Equivalence is Logspace-complete, via Binary Decision Trees
Given a logic presented in a sequent calculus, a natural question is that of
equivalence of proofs: to determine whether two given proofs are equated by any
denotational semantics, ie any categorical interpretation of the logic
compatible with its cut-elimination procedure. This notion can usually be
captured syntactically by a set of rule permutations.
Very generally, proofnets can be defined as combinatorial objects which
provide canonical representatives of equivalence classes of proofs. In
particular, the existence of proof nets for a logic provides a solution to the
equivalence problem of this logic. In certain fragments of linear logic, it is
possible to give a notion of proofnet with good computational properties,
making it a suitable representation of proofs for studying the cut-elimination
procedure, among other things.
It has recently been proved that there cannot be such a notion of proofnets
for the multiplicative (with units) fragment of linear logic, due to the
equivalence problem for this logic being Pspace-complete.
We investigate the multiplicative-additive (without unit) fragment of linear
logic and show it is closely related to binary decision trees: we build a
representation of proofs based on binary decision trees, reducing proof
equivalence to decision tree equivalence, and give a converse encoding of
binary decision trees as proofs. We get as our main result that the complexity
of the proof equivalence problem of the studied fragment is Logspace-complete.Comment: arXiv admin note: text overlap with arXiv:1502.0199
MALL proof equivalence is Logspace-complete, via binary decision diagrams
Proof equivalence in a logic is the problem of deciding whether two proofs
are equivalent modulo a set of permutation of rules that reflects the
commutative conversions of its cut-elimination procedure. As such, it is
related to the question of proofnets: finding canonical representatives of
equivalence classes of proofs that have good computational properties. It can
also be seen as the word problem for the notion of free category corresponding
to the logic.
It has been recently shown that proof equivalence in MLL (the multiplicative
with units fragment of linear logic) is PSPACE-complete, which rules out any
low-complexity notion of proofnet for this particular logic.
Since it is another fragment of linear logic for which attempts to define a
fully satisfactory low-complexity notion of proofnet have not been successful
so far, we study proof equivalence in MALL- (multiplicative-additive without
units fragment of linear logic) and discover a situation that is totally
different from the MLL case. Indeed, we show that proof equivalence in MALL-
corresponds (under AC0 reductions) to equivalence of binary decision diagrams,
a data structure widely used to represent and analyze Boolean functions
efficiently.
We show these two equivalent problems to be LOGSPACE-complete. If this
technically leaves open the possibility for a complete solution to the question
of proofnets for MALL-, the established relation with binary decision diagrams
actually suggests a negative solution to this problem.Comment: in TLCA 201
Gender, self, multiple identities, violence and magical interpretations in lovolo practices in Southern Mozambique
Includes bibliographical references (p. 237-273)
On the Resolution Semiring
In this thesis, we study a semiring structure with a product based on theresolution rule of logic programming. This mathematical object was introducedinitially in the setting of the geometry of interaction program in order to modelthe cut-elimination procedure of linear logic. It provides us with an algebraicand abstract setting, while being presented in a syntactic and concrete way, inwhich a theoretical study of computation can be carried on.We will review first the interactive interpretation of proof theory withinthis semiring via the categorical axiomatization of the geometry of interactionapproach. This interpretation establishes a way to translate functional programsinto a very simple form of logic programs.Secondly, complexity theory problematics will be considered: while thenilpotency problem in the semiring we study is undecidable in general, it willappear that certain restrictions allow for characterizations of (deterministicand non-deterministic) logarithmic space and (deterministic) polynomial timecomputation
Memoization for Unary Logic Programming: Characterizing PTIME
We give a characterization of deterministic polynomial time computation based
on an algebraic structure called the resolution semiring, whose elements can be
understood as logic programs or sets of rewriting rules over first-order terms.
More precisely, we study the restriction of this framework to terms (and logic
programs, rewriting rules) using only unary symbols. We prove it is complete
for polynomial time computation, using an encoding of pushdown automata. We
then introduce an algebraic counterpart of the memoization technique in order
to show its PTIME soundness. We finally relate our approach and complexity
results to complexity of logic programming. As an application of our
techniques, we show a PTIME-completeness result for a class of logic
programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201
Unification and Logarithmic Space: Journal Version
Soumis au numéro spécial de LMCS pour RTA/TLCA 2014 ( http://www.lmcs-online.org/ojs/specialIssues.php?id=67 )We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, an convenient way of understanding logarithmic space computation
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and Nlogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is rooted in proof
theory and more specifically linear logic and geometry of interaction. We show
how to build a model of computation in the unification algebra and then, by
means of a syntactic representation of finite permutations in the algebra, we
prove that whether an observation (the algebraic counterpart of a program)
accepts a word can be decided within logarithmic space. Finally, we show that
the construction naturally corresponds to pointer machines, a convenient way of
understanding logarithmic space computation.Comment: arXiv admin note: text overlap with arXiv:1402.432
Barbaridades e violĂȘncias
The author outlines her trajectory of intimate coexistence with the violence and the consequences inflicted on the mind and body of all the people who are involved in them. With examples from Mozambique, South Africa and Rwanda and violence linked to war, hunger, HIV / AIDS and gender, she articulates, through fragments of her experiences, the different layers and forms of violence that afflict the most unprotected. The approach of physical violence, structural violence, symbolic violence and its various combinations destroy human beings and, above all, those who have to live with the multiplicity of their forms. The proposal is to find ways to develop a new ethic of citizenship, empathy and solidarity that seeks to disarm these violences.A autora delineia a sua trajetĂłria de convivĂȘncia Ăntima com as violĂȘncias e com as consequĂȘncias infligidas na mente e no corpo de todas as pessoas que estĂŁo envolvidas nelas. Com exemplo de Moçambique, Ăfrica do Sul e Ruanda e violĂȘncias ligadas a guerra, a fome, ao HIV/AIDS e ao gĂȘnero ela articula, percorrendo fragmentos de suas experiĂȘncias, as diferentes camadas e formas de violĂȘncia que afligem os/as mais desemparados/as. A aproximação da violĂȘncia fĂsica, da violĂȘncia estrutural, da violĂȘncia simbĂłlica e das suas vĂĄrias combinaçÔes destroem os seres humanas e, sobretudo, os/as que tĂȘm de conviver com a multiplicidade das suas formas. A proposta Ă© de encontrar formas de desenvolver uma nova Ă©tica de cidadania, de empatia e solidariedade que procura desarmar estas violĂȘncias
Les dĂ©putĂ©s hĂ©raultais et la viticulture dans lâentre-deux-guerres : organes de dĂ©cision, relais de pouvoir, lĂ©gislation
Lâapproche du sujet et les sources Ă lâorigine de ma recherche, il y avait une volontĂ© de mâintĂ©resser Ă lâhistoire rurale de lâHĂ©rault et plus particuliĂšrement Ă un secteur qui a marquĂ© profondĂ©ment les destinĂ©es de ce territoire : la viticulture, plusieurs fois sĂ©culaire. Jâai donc entrepris dâanalyser lâĂ©volution de ce secteur en le mettant en interaction avec une passion personnelle pour lâanalyse politique. Jâai choisi la TroisiĂšme RĂ©publique qui avait Ă©tĂ©, jusquâĂ une date rĂ©cente, peu ..
Les dĂ©putĂ©s hĂ©raultais et la viticulture dans lâentre-deux-guerres : organes de dĂ©cision, relais de pouvoir, lĂ©gislation
Lâapproche du sujet et les sources Ă lâorigine de ma recherche, il y avait une volontĂ© de mâintĂ©resser Ă lâhistoire rurale de lâHĂ©rault et plus particuliĂšrement Ă un secteur qui a marquĂ© profondĂ©ment les destinĂ©es de ce territoire : la viticulture, plusieurs fois sĂ©culaire. Jâai donc entrepris dâanalyser lâĂ©volution de ce secteur en le mettant en interaction avec une passion personnelle pour lâanalyse politique. Jâai choisi la TroisiĂšme RĂ©publique qui avait Ă©tĂ©, jusquâĂ une date rĂ©cente, peu ..
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