First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

Transcendental number theory, by Alan Baker. Pp. x, 147. £4·90. 1975. SBN 0 521 20461 5 (Cambridge University Press)

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

We consider turn-based stochastic games on infinite graphs induced by game probabilistic lossy channel systems (GPLCS), the game version of probabilistic lossy channel systems (PLCS). We study games with Buchi (repeated reachability) objectives and almost-sure winning conditions. These games are pure memoryless determined and, under the assumption that the target set is regular, a symbolic representation of the set of winning states for each player can be effectively constructed. Thus, turn-based stochastic games on GPLCS are decidable. This generalizes the decidability result for PLCS-induced Markov decision processes in [10].

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Stochastic games with lossy channels

https://www.georgejpappas.org/papers/TCS-FP09.pdf

Robustness of temporal logic specifications for continuous-time signals

This paper presents algorithms for the automatic synthesis of real-time controllers by finding a winning strategy for certain games defined by the timed-automata of Alur and Dill. In such games, the outcome depends on the players' actions as well as on their timing. We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications.

On the synthesis of discrete controllers for timed systems

In modern networks, forwarding of packets often depends on the history of previously transmitted traffic. Such networks contain stateful middleboxes, whose forwarding behaviour depends on a mutable internal state. Firewalls and load balancers are typical examples of stateful middleboxes. 
This work addresses the complexity of verifying safety properties, such as isolation, in networks with finite-state middleboxes. Unfortunately, we show that even in the absence of forwarding loops, reasoning about such networks is undecidable due to interactions between middleboxes connected by unbounded ordered channels. We therefore abstract away channel ordering. This abstraction is sound for safety, and makes the problem decidable. Specifically, safety checking becomes EXPSPACE-complete in the number of hosts and middleboxes in the network. To tackle the high complexity, we identify two useful subclasses of finite-state middleboxes which admit better complexities. The simplest class includes, e.g., firewalls and permits polynomial-time verification. The second class includes, e.g., cache servers and learning switches, and makes the safety problem coNP-complete. 
Finally, we implement a tool for verifying the correctness of stateful networks.

Some Complexity Results for Stateful Network Verification

We provide a schematologically complete set of transformations for partially interpreted dataflow nets. This paper extends our results in (Inform. and Comput.124(1996), 154–167), where a schematologically complete set of transformations was provided for the nets which consist only of uninterpreted nodes and the results for partially interpreted nets were announced without proofs.

On schematological equivalence of partially interpreted dataflow networks

We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the neighborhood of a node that is reachable via a regular expression from a designated node. The logic is closed under boolean operations (entailment, negation) and has a finite model property. The key technical result is the proof of decidability. We show how to express precondition, postconditions, and loop invariants for some interesting programs. It is also possible to express properties such as disjointness of data-structures, and low-level heap mutations. Moreover, our logic can express properties of arbitrary data-structures and of an arbitrary number of pointer fields. The latter provides a way to naturally specify postconditions that relate the fields on entry to a procedure to the fields on exit. Therefore, it is possible to use the logic to automatically prove partial correctness of programs performing low-level heap mutations.

/pdf/a-logic-of-reachable-patterns-in-linked-data-structures-vb6ddsl941.pdf

A Logic of Reachable Patterns in Linked Data-Structures

Two fundamental results of classical automata theory are the Kleene theorem and the Buchi-Elgot-Trakhtenbrot theorem. Kleene's theorem states that a language of finite words is definable by a regular expression iff it is accepted by a finite state automaton. Buchi-Elgot-Trakhtenbrot's theorem states that a language of finite words is accepted by a finite-state automaton iff it is definable in the weak monadic second-order logic. Hence, the weak monadic logic and regular expressions are expressively equivalent over finite words. We generalize this to words over arbitrary linear orders.

Alexander Rabinovich

Papers

Some Complexity Results for Stateful Network Verification

On schematological equivalence of partially interpreted dataflow networks

A Logic of Reachable Patterns in Linked Data-Structures

On Expressive Power of Regular Expressions over Infinite Orders