Program schemes with deep pushdown storage.

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME

Regular Strategies in Pushdown Reachability Games

International audienceWe show that positional winning strategies in pushdown reachability games can be implemented by deterministic finite state au-tomata of exponential size. Such automata read the stack and control state of a given pushdown configuration and output the set of winning moves playable from that position. This result can originally be attributed to Kupferman, Piterman and Vardi using an approach based on two-way tree automata. We present a more direct approach that builds upon the popular saturation technique. Saturation for analysing pushdown systems has been successfully implemented by Moped and WALi. Thus, our approach has the potential for practical applications to controller-synthesis problems

Optimal Strategies in Pushdown Reachability Games

An algorithm for computing optimal strategies in pushdown reachability games was given by Cachat. We show that the information tracked by this algorithm is too coarse and the strategies constructed are not necessarily optimal. We then show that the algorithm can be refined to recover optimality. Through a further non-trivial argument the refined algorithm can be run in 2EXPTIME by bounding the play-lengths tracked to those that are at most doubly exponential. This is optimal in the sense that there exists a game for which the optimal strategy requires a doubly exponential number of moves to reach a target configuration

Generating analyzers with PAG

To produce high qualitiy code, modern compilers use global optimization algorithms based on it abstract interpretation. These algorithms are rather complex; their implementation is therfore a non-trivial task and error-prone. However, since thez are based on a common theory, they have large similar parts. We conclude that analyzer writing better should be replaced with analyzer generation. We present the tool sf PAG that has a high level functional input language to specify data flow analyses. It offers th specifications of even recursive data structures and is therfore not limited to bit vector problems. sf PAG generates efficient analyzers wich can be easily integrated in existing compilers. The analyzers are interprocedural, they can handle recursive procedures with local variables and higher order functions. sf PAG has successfully been tested by generating several analyzers (e.g. alias analysis, constant propagation, inerval analysis) for an industrial quality ANSI-C and Fortran90 compiler. This technical report consits of two parts; the first introduces the generation system and the second evaluates generated analyzers with respect to their space and time consumption. bf Keywords: data flow analysis, specification and generation of analyzers, lattice specification, abstract syntax specification, interprocedural analysis, compiler construction

Parameterised Pushdown Systems with Non-Atomic Writes

We consider the master/slave parameterised reachability problem for networks of pushdown systems, where communication is via a global store using only non-atomic reads and writes. We show that the control-state reachability problem is decidable. As part of the result, we provide a constructive extension of a theorem by Ehrenfeucht and Rozenberg to produce an NFA equivalent to certain kinds of CFG. Finally, we show that the non-parameterised version is undecidable.Comment: This is the long version of a paper appearing in FSTTCS 201

An observationally complete program logic for imperative higher-order functions

We establish a strong completeness property called observational completeness of the program logic for imperative, higher-order functions introduced in [1]. Observational completeness states that valid assertions characterise program behaviour up to observational congruence, giving a precise correspondence between operational and axiomatic semantics. The proof layout for the observational completeness which uses a restricted syntactic structure called finite canonical forms originally introduced in game-based semantics, and characteristic formulae originally introduced in the process calculi, is generally applicable for a precise axiomatic characterisation of more complex program behaviour, such as aliasing and local state