1. For 1-membrane catalytic systems (CS's), the sequential version is strictlyweaker than the parallel version in that the former defines (i.e. generates) exactly the semilinear sets, whereas the latter is known to define nonrecursivesets. 2. For 1-membrane communicating P systems (CPS's), the sequential versioncan only define a proper subclass of the semilinear sets, whereas the parallel version is known to define nonrecursive sets.3. Adding a new type of rule of the form: ab! axbyccomedcome to the CPS(a natural generalization of the rule ab! axbyccome in the original model),where x; y 2 fhere; outg, to the sequential 1-membrane CPS makes itequivalent to a vector addition system.

We consider the problems of typability and type checking in the Girard/Reynolds second-order polymorphic typed-calculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pure-terms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lower-bound complexity results for System F have been achieved, but they have remained "embarrassing open problems" 3 for System F itself. We first prove that type checking in System F is undecidable by a reduction from semi-unification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructing-terms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specif subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment maybe simulated. We develop this method, which we call \constants for free", for both the K and I calculi.

Abstract. Threads as contained in a thread algebra emerge from the behavioral abstraction from programs in an appropriate program algebra. Threads may make use of services such as stacks, and a thread using a single stack is called a pushdown thread. Equivalence of pushdown threads is shown decidable whereas pushdown thread inclusion is undecidable. This is again an example of a borderline crossing where the equivalence problem is decidable, whereas the inclusion problem is not. 1

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Abstract. We study various generalizations of reversal-bounded multicounter machines and show that they have decidable emptiness, infiniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linear-relation tests among the counters and parameterized constants (e.g., “Is ¢¤£¦¥¨§�©�¥��¤���������������� �?”, where £¦�� © are counters, and �������� � are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the verification/debugging of safety properties in infinite-state transition systems. For example, we show that (binary, forward, and backward) reachability, safety, and invariance are solvable for these machines. 1

We investigate expressiveness of a fragment of the ambient calculus, a formalism for describing distributed and mobile computations. More precisely, we study expressiveness of the pure and public ambient calculus from which the has been removed, in terms of the reachability problem of the reduction relation. Surprisingly, we show that even for this very restricted fragment, the reachability problem is not decidable. At a second step, for a slightly weaker reduction relation, we prove that reachability can be decided by reducing this problem to markings reachability for Petri nets. Finally, we show that the name-convergence problem as well as the model-checking problem turn out to be undecidable for both the original and the weaker reduction relation. 1

Abstract. We study two-way tree automata modulo equational theories. We deal with the theories of Abelian groups), idempotent commutative monoids (¡£¢¨¤£©), and the theory of exclusive-or), as well as some variants including the theory of commutative monoids). We show that the one-way automata for all these theories are closed under union and intersection, and emptiness is decidable. For two-way automata the situation is more complex. In all these theories except¡£¢¨¤£©, we show that two-way automata can be effectively reduced to one-way automata, provided some care is taken in the definition

We study various generalizations of reversal-bounded multicounter machines and show that they have decidable emptiness, inniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linear-relation tests among the counters and parameterized constants (e.g., \Is 3x 5y 2D 1 +9D 2 < 12?", where x; y are counters, and D 1 ; D 2 are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the verication /debugging of safety properties in innite-state transition systems. For example, we show that (binary, forward, and backward) reachability and safety are solvable for these machines. Key words: Counter machines, automated verication, innite-state systems, reachability 1 A short version [15] of this paper appeared in the Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science (MFCS 2000), Lecture Notes in Computer Science 1893 (Springer, Berlin, 2000) 426-435. 2 The work by Oscar H. Ibarra and Jianwen Su has been supported in part by NSF grants IRI-9700370 and IIS-9817432. 3 The work by Zhe Dang and Richard A. Kemmerer has been supported in part by the Defense Advanced Research Projects Agency (DARPA) and Rome Laboratory, Air Force Material Command, USAF, under agreement number F30602-97-1-0207. 4 The work by Tevk Bultan has been supported in part by NSF grant CCR9970976 and NSF CAREER award CCR-9984822. Preprint submitted to Elsevier Science 17 April 2001 1

Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and

Abstract. We introduce some new models of infinite-state transition systems. The basic model, called a (reversal-bounded) counter machine (CM), is a nondeterministic finite automaton augmented with finitely many reversal-bounded counters (i.e. each counter can be incremented or decremented by 1 and tested for zero, but the number of times it can change mode from nondecreasing to nonincreasing and vice-versa is bounded by a constant, independent of the computation). We extend a CM by augmenting it with some familiar data structures: (i) A pushdown counter machine (PCM) is a CM augmented with an unrestricted pushdown stack. (ii) A tape counter machine (TCM) is a CM augmented with a two-way read/write worktape that is restricted in that the number of times the head crosses the boundary between any two adjacent cells of the worktape is bounded by a constant, independent of the computation (thus, the worktape is finite-crossing). There is no bound on how long the head can remain on a cell. (iii) A queue counter machine (QCM) is a CM augmented with a queue that is restricted in that the number of alternations between non-deletion phase and non-insertion phase is bounded by a constant. A non-deletion (non-insertion) phase is a period consisting of insertions (deletions) and no-changes, i.e., the queue is idle. We show that emptiness, (binary, forward, and backward) reachability, nonsafety, and invariance for these machines are solvable. We also look at extensions of the models that allow the use of linear-relation tests among the counters and parameterized constants as “primitive ” predicates. We investigate the conditions under which these problems are still solvable. 1