134 research outputs found
Non-simplifying Graph Rewriting Termination
So far, a very large amount of work in Natural Language Processing (NLP) rely
on trees as the core mathematical structure to represent linguistic
informations (e.g. in Chomsky's work). However, some linguistic phenomena do
not cope properly with trees. In a former paper, we showed the benefit of
encoding linguistic structures by graphs and of using graph rewriting rules to
compute on those structures. Justified by some linguistic considerations, graph
rewriting is characterized by two features: first, there is no node creation
along computations and second, there are non-local edge modifications. Under
these hypotheses, we show that uniform termination is undecidable and that
non-uniform termination is decidable. We describe two termination techniques
based on weights and we give complexity bound on the derivation length for
these rewriting system.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599
Observation of implicit complexity by non confluence
We propose to consider non confluence with respect to implicit complexity. We
come back to some well known classes of first-order functional program, for
which we have a characterization of their intentional properties, namely the
class of cons-free programs, the class of programs with an interpretation, and
the class of programs with a quasi-interpretation together with a termination
proof by the product path ordering. They all correspond to PTIME. We prove that
adding non confluence to the rules leads to respectively PTIME, NPTIME and
PSPACE. Our thesis is that the separation of the classes is actually a witness
of the intentional properties of the initial classes of programs
Analysis and Diversion of Duqu's Driver
The propagation techniques and the payload of Duqu have been closely studied
over the past year and it has been said that Duqu shared functionalities with
Stuxnet. We focused on the driver used by Duqu during the infection, our
contribution consists in reverse-engineering the driver: we rebuilt its source
code and analyzed the mechanisms it uses to execute the payload while avoiding
detection. Then we diverted the driver into a defensive version capable of
detecting injections in Windows binaries, thus preventing further attacks. We
specifically show how Duqu's modified driver would have detected Duqu.Comment: Malware 2013 - 8th International Conference on Malicious and Unwanted
Software (2013
Intensional properties of polygraphs
We present polygraphic programs, a subclass of Albert Burroni's polygraphs,
as a computational model, showing how these objects can be seen as first-order
functional programs. We prove that the model is Turing complete. We use
polygraphic interpretations, a termination proof method introduced by the
second author, to characterize polygraphic programs that compute in polynomial
time. We conclude with a characterization of polynomial time functions and
non-deterministic polynomial time functions.Comment: Proceedings of TERMGRAPH 2007, Electronic Notes in Computer Science
(to appear), 12 pages, minor changes from previous versio
Polynomials over the reals are safe for program interpretations
In the field of implicit computational complexity, we are con- sidering in this paper the fruitful branch of interpretation methods. Due to their good intensional properties, they have been widely developped. Among usual issues is the synthesis problem which has been solved by the use of Tarski's decision procedure, and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (well-) ordering of N employed to bound the complexity of programs. We show that, actually, polynomials over the reals benefit from some properties that allows their safe use for complexity. We illustrate this by two char- acterizations, one of PTIME and one of PSPACE
Course of value distinguishes the intentionality of programming languages
International audienceIn this contribution, we propose to study the transformation of first order programs by course of value recursion. Our motivation is to show that this transformation provides a separation criterion for the intentionality of sets of programs. As an illustration, we consider two variants of the multiset path ordering, for the first, terms in recursive calls are compared with respect to the subterm property, for the second with respect to embedding. Under a quasi-interpretation, both characterize Ptime, the latter characterization being a new result. Once applied the transformation, we get respec- tively Ptime and Pspace thus proving that the latter set of programs contains more algorithms
Monotone interpretations
Nous considérons une nouvelle classe d'interprétation des systèmes de réécriture. Nous montrons qu'elle bénéficie de bonne propriété intentionnelles
Non-size increasing Graph Rewriting for Natural Language Processing
International audienceA very large amount of work in Natural Language Processing use tree structure as the first class citizen mathematical structures to represent linguistic structures such as parsed sentences or feature structures. However, some linguistic phenomena do not cope properly with trees: for instance, in the sentence "Max decides to leave", "Max" is the subject of the both predicates "to decide" and "to leave". Tree-based linguistic formalisms generally use some encoding to manage sentences like the previous example. In former papers, we discussed the interest to use graphs rather than trees to deal with linguistic structures and we have shown how Graph Rewriting could be used for their processing, for instance in the transformation of the sentence syntax into its semantics. Our experiments have shown that Graph Rewriting applications to Natural Language Processing do not require the full computational power of the general Graph Rewriting setting. The most important observation is that all graph vertices in the final structures are in some sense "predictable" from the input data and so, we can consider the framework of Non-size increasing Graph Rewriting. In our previous papers, we have formally described the Graph Rewriting calculus we used and our purpose here is to study the theoretical aspect of termination with respect to this calculus. In our framework, we show that uniform termination is undecidable and that non-uniform termination is decidable. We define termination techniques based on weight, we prove the termination of weighted rewriting systems and we give complexity bounds on derivation lengths for these rewriting systems
Some programming languages for LOGSPACE and PTIME
We propose two characterizations of complexity classes by means of programming languages. The first concerns Logspace while the second leads to Ptime. This latter characterization shows that adding a choice command to a Ptime language (the language WHILE of Jones) may not necessarily provide NPtime computations. The result is close to Cook who used “auxiliary push-down automata”. Logspace is obtained through a decidable mechanism of tiering. It is based on an analysis of deforestation due to Wadler in. We get also a characterization of NLogspace
Quasi-interpretations a way to control resources
International audienceThis paper presents in a reasoned way our works on resource analysis by quasi- interpretations. The controlled resources are typically the runtime, the runspace or the size of a result in a program execution. Quasi-interpretations allow analyzing system complexity. A quasi-interpretation is a numerical assignment, which provides an upper bound on computed func- tions and which is compatible with the program operational semantics. Quasi- interpretation method offers several advantages: (i) It provides hints in order to optimize an execution, (ii) it gives resource certificates, and (iii) finding quasi- interpretations is decidable for a broad class which is relevant for feasible com- putations. By combining the quasi-interpretation method with termination tools (here term orderings), we obtained several characterizations of complexity classes starting from Ptime and Pspace
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