3,044 research outputs found
Underapproximation of Procedure Summaries for Integer Programs
We show how to underapproximate the procedure summaries of recursive programs
over the integers using off-the-shelf analyzers for non-recursive programs. The
novelty of our approach is that the non-recursive program we compute may
capture unboundedly many behaviors of the original recursive program for which
stack usage cannot be bounded. Moreover, we identify a class of recursive
programs on which our method terminates and returns the precise summary
relations without underapproximation. Doing so, we generalize a similar result
for non-recursive programs to the recursive case. Finally, we present
experimental results of an implementation of our method applied on a number of
examples.Comment: 35 pages, 3 figures (this report supersedes the STTT version which in
turn supersedes the TACAS'13 version
Interprocedural Reachability for Flat Integer Programs
We study programs with integer data, procedure calls and arbitrary call
graphs. We show that, whenever the guards and updates are given by octagonal
relations, the reachability problem along control flow paths within some
language w1* ... wd* over program statements is decidable in Nexptime. To
achieve this upper bound, we combine a program transformation into the same
class of programs but without procedures, with an Np-completeness result for
the reachability problem of procedure-less programs. Besides the program, the
expression w1* ... wd* is also mapped onto an expression of a similar form but
this time over the transformed program statements. Several arguments involving
context-free grammars and their generative process enable us to give tight
bounds on the size of the resulting expression. The currently existing gap
between Np-hard and Nexptime can be closed to Np-complete when a certain
parameter of the analysis is assumed to be constant.Comment: 38 pages, 1 figur
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
Hierarchies of hyper-AFLs
For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) B(K) is the smallest full hyper-AFL containing K; a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a full basic-AFL. If K is not a full basic-AFL, then the smallest full basic-AFL containing K is the union of an infinite hierarchy of full hyper-AFLs. If K is a full principal basic-AFL (such as INDEX, the family of indexed languages), then the largest full AFL properly contained in K is a full basic-AFL. There is a full basic-AFL lying properly in between the smallest full basic-AFL and the largest full basic-AFL in INDEX
A translational theorem for the class of EOL languages
If K is not a context-free language, then sh(K, a*) is not an EOL language (where sh(K1, K2) denotes the shuffle of the languages K1 and K2, and a is a symbol not in the alphabet of K). Hence the class of context-free languages is the largest full AFL inside the class of EOL languages
Repotting the Geraniums: On Nested Graph Transformation Rules
We propose a scheme for rule amalgamation based on nested graph predicates. Essentially, we extend all the graphs in such a predicate with right hand sides. Whenever such an enriched nested predicate matches (i.e., is satisfied by) a given host graph, this results in many individual match morphisms, and thus many “small” rule applications. The total effect is described by the amalgamated rule. This makes for a smooth, uniform and very powerful amalgamation scheme, which we demonstrate on a number of examples. Among the examples is the following, which we believe to be inexpressible in very few other parallel rule formalism proposed in the literature: repot all flowering geraniums whose pots have cracked.\u
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