116 research outputs found
Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting
We model collapsible and ordered pushdown systems with term rewriting, by
encoding higher-order stacks and multiple stacks into trees. We show a uniform
inverse preservation of recognizability result for the resulting class of term
rewriting systems, which is obtained by extending the classic saturation-based
approach. This result subsumes and unifies similar analyses on collapsible and
ordered pushdown systems. Despite the rich literature on inverse preservation
of recognizability for term rewrite systems, our result does not seem to follow
from any previous study.Comment: in Proc. of FRE
Rewriting Approximations For Properties Verification Over CCS Specifications
This paper presents a way to verify CCS (without renaming) specifications using tree regular model checking. From a term rewriting system and a tree automaton representing the semantics of CCS and equations of a CCS specification to analyse, an over-approximation of the set of reachable terms is computed from an initial configuration. This set, in the framework of CCS, represents an over-approximation of all states (modulo bisimulation) and action sequences the CCS specification can reach. The approach described in this paper can be fully automated. It is illustrated with the Alternating Bit Protocol and with hardware components specifications
Reachability Analysis of Innermost Rewriting
We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs and, several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of
terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. The proposed algorithm has been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy
Termination of Rewriting with Right-Flat Rules Modulo Permutative Theories
We present decidability results for termination of classes of term rewriting
systems modulo permutative theories. Termination and innermost termination
modulo permutative theories are shown to be decidable for term rewrite systems
(TRS) whose right-hand side terms are restricted to be shallow (variables occur
at depth at most one) and linear (each variable occurs at most once). Innermost
termination modulo permutative theories is also shown to be decidable for
shallow TRS. We first show that a shallow TRS can be transformed into a flat
(only variables and constants occur at depth one) TRS while preserving
termination and innermost termination. The decidability results are then proved
by showing that (a) for right-flat right-linear (flat) TRS, non-termination
(respectively, innermost non-termination) implies non-termination starting from
flat terms, and (b) for right-flat TRS, the existence of non-terminating
derivations starting from a given term is decidable. On the negative side, we
show PSPACE-hardness of termination and innermost termination for shallow
right-linear TRS, and undecidability of termination for flat TRS.Comment: 20 page
On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings
In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs
The Confluence Problem for Flat TRSs
International audienceWe prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one
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